Renormalization And Geometry In One Dimensional And Complex Dynamics

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Renormalization And Geometry In One-dimensional And Complex Dynamics

Yunping Jiang
Renormalization And Geometry In One dimensional And Complex Dynamics Book PDF

Author : Yunping Jiang
Publisher : World Scientific
Page : 327 pages
File Size : 55,8 Mb
Release : 1996-09-20
Category : Science
ISBN : 9789814500173

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Renormalization And Geometry In One-dimensional And Complex Dynamics by Yunping Jiang Pdf

About one and a half decades ago, Feigenbaum observed that bifurcations, from simple dynamics to complicated ones, in a family of folding mappings like quadratic polynomials follow a universal rule (Coullet and Tresser did some similar observation independently). This observation opened a new way to understanding transition from nonchaotic systems to chaotic or turbulent system in fluid dynamics and many other areas. The renormalization was used to explain this observed universality. This research monograph is intended to bring the reader to the frontier of this active research area which is concerned with renormalization and rigidity in real and complex one-dimensional dynamics. The research work of the author in the past several years will be included in this book. Most recent results and techniques developed by Sullivan and others for an understanding of this universality as well as the most basic and important techniques in the study of real and complex one-dimensional dynamics will also be included here.

Renormalization and Geometry in One-dimensional and Complex Dynamics

Yunping Jiang
Renormalization and Geometry in One dimensional and Complex Dynamics Book PDF

Author : Yunping Jiang
Publisher : World Scientific
Page : 344 pages
File Size : 49,9 Mb
Release : 1996
Category : Science
ISBN : 9810223269

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Renormalization and Geometry in One-dimensional and Complex Dynamics by Yunping Jiang Pdf

The book is intended to help under- and postgraduate students and young scientists in the correct application of NMR to the solution of physico-chemical problems concerning the study of equilibria in solution. The first part of the book (Chapters 1–3) is a trivium, but should enable a student to design and conduct simple physico-chemical NMR experiments. The following chapters give illustrative material on the physico-chemical applications of NMR of increasing complexity. These chapters include the problem of determination of equilibrium and rate constants in solution, the study of paramagnetism using NMR, the application of Dynamic NMR techniques and relaxation measurements. A multipurpose nonlinear regression program is supplied (on disc for PC) and is referred to throughout the book.

Complex Dynamics and Renormalization

Curtis T. McMullen
Complex Dynamics and Renormalization Book PDF

Author : Curtis T. McMullen
Publisher : Unknown
Page : 214 pages
File Size : 42,9 Mb
Release : 1994
Category : Science
ISBN : 0691029822

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Complex Dynamics and Renormalization by Curtis T. McMullen Pdf

Addressing researchers and graduate students in the active meeting ground of analysis, geometry, and dynamics, this book presents a study of renormalization of quadratic polynomials and a rapid introduction to techniques in complex dynamics. Its central concern is the structure of an infinitely renormalizable quadratic polynomial f(z) = z2 + c. As discovered by Feigenbaum, such a mapping exhibits a repetition of form at infinitely many scales. Drawing on universal estimates in hyperbolic geometry, this work gives an analysis of the limiting forms that can occur and develops a rigidity criterion for the polynomial f. This criterion supports general conjectures about the behavior of rational maps and the structure of the Mandelbrot set. The course of the main argument entails many facets of modern complex dynamics. Included are foundational results in geometric function theory, quasiconformal mappings, and hyperbolic geometry. Most of the tools are discussed in the setting of general polynomials and rational maps.

Julia Sets and Complex Singularities of Free Energies

Jianyong Qiao
Julia Sets and Complex Singularities of Free Energies Book PDF

Author : Jianyong Qiao
Publisher : American Mathematical Soc.
Page : 89 pages
File Size : 53,7 Mb
Release : 2015-02-06
Category : Mathematics
ISBN : 9781470409821

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Julia Sets and Complex Singularities of Free Energies by Jianyong Qiao Pdf

The author studies a family of renormalization transformations of generalized diamond hierarchical Potts models through complex dynamical systems. He proves that the Julia set (unstable set) of a renormalization transformation, when it is treated as a complex dynamical system, is the set of complex singularities of the free energy in statistical mechanics. He gives a sufficient and necessary condition for the Julia sets to be disconnected. Furthermore, he proves that all Fatou components (components of the stable sets) of this family of renormalization transformations are Jordan domains with at most one exception which is completely invariant. In view of the problem in physics about the distribution of these complex singularities, the author proves here a new type of distribution: the set of these complex singularities in the real temperature domain could contain an interval. Finally, the author studies the boundary behavior of the first derivative and second derivative of the free energy on the Fatou component containing the infinity. He also gives an explicit value of the second order critical exponent of the free energy for almost every boundary point.

Dynamics, Games and Science

Jean-Pierre Bourguignon,Rolf Jeltsch,Alberto Adrego Pinto,Marcelo Viana
Dynamics Games and Science Book PDF

Author : Jean-Pierre Bourguignon,Rolf Jeltsch,Alberto Adrego Pinto,Marcelo Viana
Publisher : Springer
Page : 772 pages
File Size : 43,8 Mb
Release : 2015-07-24
Category : Mathematics
ISBN : 9783319161181

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Dynamics, Games and Science by Jean-Pierre Bourguignon,Rolf Jeltsch,Alberto Adrego Pinto,Marcelo Viana Pdf

The focus of this volume is research carried out as part of the program Mathematics of Planet Earth, which provides a platform to showcase the essential role of mathematics in addressing problems of an economic and social nature and creating a context for mathematicians and applied scientists to foster mathematical and interdisciplinary developments that will be necessary to tackle a myriad of issues and meet future global economic and social challenges. Earth is a planet with dynamic processes in its mantle, oceans and atmosphere creating climate, causing natural disasters and influencing fundamental aspects of life and life-supporting systems. In addition to these natural processes, human activity has developed highly complex systems, including economic and financial systems; the World Wide Web; frameworks for resource management, transportation, energy production and utilization; health care delivery, and social organizations. This development has increased to the point where it impacts the stability and equilibrium in human societies. Issues such as financial and economic crisis, sustainability, management of resources, risk analysis, and global integration have come to the fore. Written by some of the world’s leading specialists, this book presents the proceedings of the International Conference and Advanced School Planet Earth, Dynamics, Games and Science II, held in Lisbon, Portugal, 28 August -6 September 2013, which was organized by the International Center of Mathematics (CIM) as a partner institution of the international program Mathematics of Planet Earth 2013. The book describes the state of the art in advanced research and ultimate techniques in modeling natural, economic and social phenomena. It constitutes a tool and a framework for researchers and graduate students, both in mathematics and applied sciences, focusing mainly on dynamical systems, game theory and applied sciences.

Dynamics, Games and Science II

Mauricio Matos Peixoto,Alberto Adrego Pinto,David A. Rand
Dynamics Games and Science II Book PDF

Author : Mauricio Matos Peixoto,Alberto Adrego Pinto,David A. Rand
Publisher : Springer Science & Business Media
Page : 757 pages
File Size : 50,9 Mb
Release : 2011-05-27
Category : Mathematics
ISBN : 9783642147883

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Dynamics, Games and Science II by Mauricio Matos Peixoto,Alberto Adrego Pinto,David A. Rand Pdf

Dynamics, Games and Science I and II are a selection of surveys and research articles written by leading researchers in mathematics. The majority of the contributions are on dynamical systems and game theory, focusing either on fundamental and theoretical developments or on applications to modeling in biology, ecomonics, engineering, finances and psychology. The papers are based on talks given at the International Conference DYNA 2008, held in honor of Mauricio Peixoto and David Rand at the University of Braga, Portugal, on September 8-12, 2008. The aim of these volumes is to present cutting-edge research in these areas to encourage graduate students and researchers in mathematics and other fields to develop them further.

Combinatorial Dynamics and Entropy in Dimension One

Lluís Alsedà,Jaume Llibre,Michal Misiurewicz
Combinatorial Dynamics and Entropy in Dimension One Book PDF

Author : Lluís Alsedà,Jaume Llibre,Michal Misiurewicz
Publisher : World Scientific Publishing Company
Page : 432 pages
File Size : 52,6 Mb
Release : 2000-10-31
Category : Science
ISBN : 9789813105591

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Combinatorial Dynamics and Entropy in Dimension One by Lluís Alsedà,Jaume Llibre,Michal Misiurewicz Pdf

This book introduces the reader to the two main directions of one-dimensional dynamics. The first has its roots in the Sharkovskii theorem, which describes the possible sets of periods of all cycles (periodic orbits) of a continuous map of an interval into itself. The whole theory, which was developed based on this theorem, deals mainly with combinatorial objects, permutations, graphs, etc.; it is called combinatorial dynamics. The second direction has its main objective in measuring the complexity of a system, or the degree of “chaos” present in it; for that the topological entropy is used. The book analyzes the combinatorial dynamics and topological entropy for the continuous maps of either an interval or the circle into itself.

Dynamical Systems

Yunping Jiang,Lan Wen
Dynamical Systems Book PDF

Author : Yunping Jiang,Lan Wen
Publisher : World Scientific
Page : 372 pages
File Size : 45,6 Mb
Release : 1999-12-16
Category : Electronic
ISBN : 9789814543279

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Dynamical Systems by Yunping Jiang,Lan Wen Pdf

This volume constitutes the proceedings of the International Conference on Dynamical Systems in Honor of Prof. Liao Shantao (1920–97). The Third World Academy of Sciences awarded the first ever mathematics prize in 1985 to Prof. Liao in recognition of his foundational work in differentiable dynamical systems and his work in periodic transformation of spheres. The conference was held in Beijing in August 1998. There were about 90 participants, and nearly 60 talks were delivered. The topics covered include differentiable dynamics, topological dynamics, hamiltonian dynamics, complex dynamics, ergodic and stochastic dynamics, and fractals theory. Dynamical systems is a field with many difficult problems, and techniques are being developed to deal with those problems. This volume contains original studies of great mathematical depth and presents some of the fascinating numerical experiments. Contents: The Dynamics of the Henon-Like Maps (Y-L Cao)Nonchaos for Substitution Minimal Systems (Q-J Fan et al.)A Note on the Obstruction Sets of Discrete Systems (S-B Gan)Topological Pressure of Continuous Flows Without Fixed Points (L-F He et al.)Nonlinearity, Quasisymmetry, Differentiability, and Rigidity in One-Dimensional Dynamics (Y-P Jiang)The Stability of the Equilibrium of Planar Hamiltonian Systems (B Liu)Existence and Uniqueness of Analytic Solutions of Iterative Functional Equations (J-H Mai & X-H Liu)On Bimodal Collet-Eckmann Maps (L-Y Wang)An Introduction to the C1 Connecting Lemma (L Wen)Partial Entropy, Bundle-Like Entropy and Topological Entropy (F-P Zeng)and other papers Readership: Research mathematicians and graduates in analysis and differential equations. Keywords:Dynamical Systems;Periodic Transformation;Topological Dynamics;Hamiltonian Dynamics;Complex Dynamics;Ergodic;Stochastic Dynamics;Fractals Theory;Henon-Like Maps;Fixed Points;Nonlinearity;Quasisymmetry;Planar Hamiltonian Systems;Analytic Solutions;Iterative Functional Equations;Partial Entropy;Bundle-Like Entropy;Topological Entropy

Conformal Dynamics and Hyperbolic Geometry

Francis Bonahon
Conformal Dynamics and Hyperbolic Geometry Book PDF

Author : Francis Bonahon
Publisher : American Mathematical Soc.
Page : 266 pages
File Size : 42,7 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821853481

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Conformal Dynamics and Hyperbolic Geometry by Francis Bonahon Pdf

This volume contains the proceedings of the Conference on Conformal Dynamics and Hyperbolic Geometry, held October 21-23, 2010, in honor of Linda Keen's 70th birthday. This volume provides a valuable introduction to problems in conformal and hyperbolic geometry and one dimensional, conformal dynamics. It includes a classic expository article by John Milnor on the structure of hyperbolic components of the parameter space for dynamical systems arising from the iteration of polynomial maps in the complex plane. In addition there are foundational results concerning Teichmuller theory, the geometry of Fuchsian and Kleinian groups, domain convergence properties for the Poincare metric, elaboration of the theory of the universal solenoid, the geometry of dynamical systems acting on a circle, and realization of Thompson's group as a mapping class group for a uniformly asymptotically affine circle endomorphism. The portion of the volume dealing with complex dynamics will appeal to a diverse group of mathematicians. Recently many researchers working in a wide range of topics, including topology, algebraic geometry, complex analysis, and dynamical systems, have become involved in aspects of this field.

Progress in Holomorphic Dynamics

Hartje Kriete
Progress in Holomorphic Dynamics Book PDF

Author : Hartje Kriete
Publisher : CRC Press
Page : 204 pages
File Size : 47,5 Mb
Release : 1998-05-20
Category : Mathematics
ISBN : 0582323886

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Progress in Holomorphic Dynamics by Hartje Kriete Pdf

In the last few decades, complex dynamical systems have received widespread public attention and emerged as one of the most active fields of mathematical research. Starting where other monographs in the subject end, Progress in Holomorphic Dynamics advances the theoretical aspects and recent results in complex dynamical systems, with particular emphasis on Siegel discs. Organized into four parts, the papers in this volume grew out of three workshops: two hosted by the Georg-August-Universität Göttingen and one at the "Mathematisches Forschungsinstitut Oberwolfach." Part I addresses linearization. The authors review Yoccoz's proof that the Brjuno condition is the optimal condition for linearizability of indifferent fixed points and offer a treatment of Perez-Marco's refinement of Yoccoz's work. Part II discusses the conditions necessary for the boundary of a Siegel disc to contain a critical point, builds upon Herman's work, and offers a survey of the state-of-the-art regarding the boundaries of Siegel discs. Part III deals with the topology of Julia sets with Siegel discs and contains a remarkable highlight: C.L. Petersen establishes the existence of Siegel discs of quadratic polynomials with a locally connected boundary. Keller, taking a different approach, explains the relations between locally connected "real Julia sets" with Siegel discs and the abstract concepts of kneading sequences and itineraries. Part IV closes the volume with four papers that review the different directions of present research in iteration theory. It includes discussions on the relations between commuting rational functions and their Julia sets, interactions between the iteration of polynomials and the iteration theory of entire transcendental functions, a deep analysis of the topology of the limbs of the Mandelbrot set, and an overview of complex dynamics in higher dimensions.

Geometry of Nonholonomically Constrained Systems

Richard H. Cushman,Hans Duistermaat,J?drzej ?niatycki
Geometry of Nonholonomically Constrained Systems Book PDF

Author : Richard H. Cushman,Hans Duistermaat,J?drzej ?niatycki
Publisher : World Scientific
Page : 421 pages
File Size : 48,5 Mb
Release : 2010
Category : Mathematics
ISBN : 9789814289481

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Geometry of Nonholonomically Constrained Systems by Richard H. Cushman,Hans Duistermaat,J?drzej ?niatycki Pdf

This book gives a modern differential geometric treatment of linearly nonholonomically constrained systems. It discusses in detail what is meant by symmetry of such a system and gives a general theory of how to reduce such a symmetry using the concept of a differential space and the almost Poisson bracket structure of its algebra of smooth functions. The above theory is applied to the concrete example of Carathodory's sleigh and the convex rolling rigid body. The qualitative behavior of the motion of the rolling disk is treated exhaustively and in detail. In particular, it classifies all motions of the disk, including those where the disk falls flat and those where it nearly falls flat. The geometric techniques described in this book for symmetry reduction have not appeared in any book before. Nor has the detailed description of the motion of the rolling disk. In this respect, the authors are trail-blazers in their respective fields.

Methods in Equivariant Bifurcations and Dynamical Systems

Pascal Chossat,Reiner Lauterbach
Methods in Equivariant Bifurcations and Dynamical Systems Book PDF

Author : Pascal Chossat,Reiner Lauterbach
Publisher : World Scientific Publishing Company
Page : 420 pages
File Size : 46,9 Mb
Release : 2000-02-28
Category : Science
ISBN : 9789813105447

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Methods in Equivariant Bifurcations and Dynamical Systems by Pascal Chossat,Reiner Lauterbach Pdf

This invaluable book presents a comprehensive introduction to bifurcation theory in the presence of symmetry, an applied mathematical topic which has developed considerably over the past twenty years and has been very successful in analysing and predicting pattern formation and other critical phenomena in most areas of science where nonlinear models are involved, like fluid flow instabilities, chemical waves, elasticity and population dynamics. The book has two aims. One is to expound the mathematical methods of equivariant bifurcation theory. Beyond the classical bifurcation tools, such as center manifold and normal form reductions, the presence of symmetry requires the introduction of the algebraic and geometric formalism of Lie group theory and transformation group methods. For the first time, all these methods in equivariant bifurcations are presented in a coherent and self-consistent way in a book. The other aim is to present the most recent ideas and results in this theory, in relation to applications. This includes bifurcations of relative equilibria and relative periodic orbits for compact and noncompact group actions, heteroclinic cycles and forced symmetry-breaking perturbations. Although not all recent contributions could be included and a choice had to be made, a rather complete description of these new developments is provided. At the end of every chapter, exercises are offered to the reader.

Rayleigh-Bénard Convection

A V Getling
Rayleigh B nard Convection Book PDF

Author : A V Getling
Publisher : World Scientific
Page : 256 pages
File Size : 43,9 Mb
Release : 1998-03-06
Category : Science
ISBN : 9789814498975

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Rayleigh-Bénard Convection by A V Getling Pdf

This invaluable book presents a concise but systematic account of the formation of spatial flow structures in a horizontal fluid layer heated from below. Flows of this type, known as Rayleigh-Bénard convection, show important features of behaviour inherent not only in various hydrodynamic-instability phenomena but also in nonlinear pattern-forming processes in other contexts. The book describes the basic methods of investigating convection patterns, and the types of two- and three-dimensional flows, pattern defects, and sequences of convection-regime changes. The author pays special attention to the question of how various factors (mainly reducible to initial and boundary conditions) determine the shapes and sizes of the structures which develop. In this way, the role of order and disorder in flow patterns, as a factor strongly affecting the character of the evolution of structures, is revealed. The presentation emphasizes the physical picture of these phenomena, without excessive mathematical detail. Contents:Basic Concepts:The Boussinesq ApproximationThe Rayleigh-Bénard ProblemLinear AnalysisNonlinear Regimes and BifurcationsPlanforms of Convection CellsInvestigation Tools:ExperimentTheoretical ApproachesBasic Types of Convective-Flow Structures:Two-Dimensional Rolls and Three-Dimensional CellsPatterns of Quasi-Two-Dimensional RollsConvection Textures. Roll-Pattern DefectsConvection-Regimes:Regime DiagramPhase TurbulenceSpiral-Defect ChaosSelection of the Wavenumbers of Convection Rolls:Wavenumbers in Experiments with Random Initial DisturbancesSearches for Universal Selection CriteriaStability of Two-Dimensional Roll FlowsLyapunov Functional and Selection“Selection Mechanisms”Peculiarities of Stratification and Vertical Structure of Convection:Effects of Strong Temperature Dependence of ViscosityPenetrative ConvectionSmall-Scale Motions in a Globally Unstable LayerAstro- and Geophysical Applications Readership: Specialists in nonlinear phenomena, hydrodynamic stability, thermophysics, astrophysics, atmospheric and oceanic physics, applied science and technology; graduate students in physics, mechanics and mathematics. keywords:Rayleigh-Bénard Convection;Thermal Convection;Horizontal Layer;Structures;Patterns;Regimes;Wavenumber Selection “There are no other texts covering similar ground and … this book will be especially useful to any graduate student who wishes to understand modern developments in the theory of convection.” Journal of Fluid Mechanics “… there is no denying that the convective regime of moderate amplitude, where pattern theory works well, is well worth a book of its own, and Getling's is of about the right thickness.” Physics Today “…written competently and authoritatively … by far the best available monograph on Rayleigh-Bénard convection.” European Journal of Mechanics

Geometrical Theory of Dynamical Systems and Fluid Flows (revised Edition)

Anonim
Geometrical Theory of Dynamical Systems and Fluid Flows revised Edition Book PDF

Author : Anonim
Publisher : World Scientific
Page : 444 pages
File Size : 49,5 Mb
Release : 2009
Category : Fluid dynamics
ISBN : 9789814282253

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Geometrical Theory of Dynamical Systems and Fluid Flows (revised Edition) by Anonim Pdf

"This is an introductory textbook on the geometrical theory of dynamical systems, fluid flows and certain integrable systems. The topics are interdisciplinary and extend from mathematics, mechanics and physics to mechanical engineering, and the approach is very fundamental. The main theme of this book is a unified formulation to understand dynamical evolutions of physical systems within mathematical ideas of Riemannian geometry and Lie groups by using well-known examples. Underlying mathematical concepts include transformation invariance, covariant derivative, geodesic equation and curvature tensors on the basis of differential geometry, theory of Lie groups and integrability. These mathematical theories are applied to physical systems such as free rotation of a top, surface wave of shallow water, action principle in mechanics, diffeomorphic flow of fluids, vortex motions and some integrable systems. In the latest edition, a new formulation of fluid flows is also presented in a unified fashion on the basis of the gauge principle of theoretical physics and principle of least action along with new type of Lagrangians. A great deal of effort has been directed toward making the description elementary, clear and concise, to provide beginners easy access to the topics."-

Integrability and Nonintegrability of Dynamical Systems

Alain Goriely
Integrability and Nonintegrability of Dynamical Systems Book PDF

Author : Alain Goriely
Publisher : World Scientific
Page : 438 pages
File Size : 43,7 Mb
Release : 2001
Category : Science
ISBN : 981281194X

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Integrability and Nonintegrability of Dynamical Systems by Alain Goriely Pdf

This invaluable book examines qualitative and quantitative methods for nonlinear differential equations, as well as integrability and nonintegrability theory. Starting from the idea of a constant of motion for simple systems of differential equations, it investigates the essence of integrability, its geometrical relevance and dynamical consequences. Integrability theory is approached from different perspectives, first in terms of differential algebra, then in terms of complex time singularities and finally from the viewpoint of phase geometry (for both Hamiltonian and non-Hamiltonian systems). As generic systems of differential equations cannot be exactly solved, the book reviews the different notions of nonintegrability and shows how to prove the nonexistence of exact solutions and/or a constant of motion. Finally, nonintegrability theory is linked to dynamical systems theory by showing how the property of complete integrability, partial integrability or nonintegrability can be related to regular and irregular dynamics in phase space. Contents: Integrability: An Algebraic Approach; Integrability: An Analytic Approach; Polynomial and Quasi-Polynomial Vector Fields; Nonintegrability; Hamiltonian Systems; Nearly Integrable Dynamical Systems; Open Problems. Readership: Mathematical and theoretical physicists and astronomers and engineers interested in dynamical systems.