Combinatorial Dynamics And Entropy In Dimension One

Author : Lluís Alsedà,Jaume Llibre,Michal Misiurewicz
Publisher : World Scientific Publishing Company
Page : 432 pages
File Size : 42,9 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.

Author : Lluis Alseda,Jaume Llibre,M. Misiurewiczl
Publisher : World Scientific Publishing Company
Page : 128 pages
File Size : 40,6 Mb
Release : 1993-06-01
Category : Mathematics
ISBN : 9810242301

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Combinatorial Dyns and Entropy in Di. by Lluis Alseda,Jaume Llibre,M. Misiurewiczl Pdf

Author : Ll Alsedà
Publisher : Unknown
Page : 128 pages
File Size : 47,7 Mb
Release : 2000
Category : Electronic
ISBN : 9812813365

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Combinatorial Dynamics and Entropy in Dimension One by Ll Alsedà Pdf

Author : Welington de Melo,Sebastian van Strien
Publisher : Springer Science & Business Media
Page : 616 pages
File Size : 49,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642780431

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One-Dimensional Dynamics by Welington de Melo,Sebastian van Strien Pdf

One-dimensional dynamics has developed in the last decades into a subject in its own right. Yet, many recent results are inaccessible and have never been brought together. For this reason, we have tried to give a unified ac count of the subject and complete proofs of many results. To show what results one might expect, the first chapter deals with the theory of circle diffeomorphisms. The remainder of the book is an attempt to develop the analogous theory in the non-invertible case, despite the intrinsic additional difficulties. In this way, we have tried to show that there is a unified theory in one-dimensional dynamics. By reading one or more of the chapters, the reader can quickly reach the frontier of research. Let us quickly summarize the book. The first chapter deals with circle diffeomorphisms and contains a complete proof of the theorem on the smooth linearizability of circle diffeomorphisms due to M. Herman, J.-C. Yoccoz and others. Chapter II treats the kneading theory of Milnor and Thurstonj also included are an exposition on Hofbauer's tower construction and a result on fuB multimodal families (this last result solves a question posed by J. Milnor).

Author : Huimin Xie
Publisher : World Scientific
Page : 290 pages
File Size : 43,9 Mb
Release : 1996
Category : Science
ISBN : 9789810223984

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Grammatical Complexity and One-dimensional Dynamical Systems by Huimin Xie Pdf

A combinatorial method is developed in this book to explore the mysteries of chaos, which has became a topic of science since 1975. Using tools from theoretical computer science, formal languages and automata, the complexity of symbolic behaviors of dynamical systems is classified and analysed thoroughly. This book is mainly devoted to explanation of this method and apply it to one-dimensional dynamical systems, including the circle and interval maps, which are typical in exhibiting complex behavior through simple iterated calculations. The knowledge for reading it is self-contained in the book.

Author : Santiago Ibáñez,Jesús S. Pérez del Río,Antonio Pumariño,J. Ángel Rodríguez
Publisher : Springer Science & Business Media
Page : 426 pages
File Size : 40,9 Mb
Release : 2013-09-20
Category : Mathematics
ISBN : 9783642388309

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Progress and Challenges in Dynamical Systems by Santiago Ibáñez,Jesús S. Pérez del Río,Antonio Pumariño,J. Ángel Rodríguez Pdf

This book contains papers based on talks given at the International Conference Dynamical Systems: 100 years after Poincaré held at the University of Oviedo, Gijón in Spain, September 2012. It provides an overview of the state of the art in the study of dynamical systems. This book covers a broad range of topics, focusing on discrete and continuous dynamical systems, bifurcation theory, celestial mechanics, delay difference and differential equations, Hamiltonian systems and also the classic challenges in planar vector fields. It also details recent advances and new trends in the field, including applications to a wide range of disciplines such as biology, chemistry, physics and economics. The memory of Henri Poincaré, who laid the foundations of the subject, inspired this exploration of dynamical systems. In honor of this remarkable mathematician, theoretical physicist, engineer and philosopher, the authors have made a special effort to place the reader at the frontiers of current knowledge in the discipline.

Author : A.N. Sharkovsky,S.F. Kolyada,A.G. Sivak,V.V. Fedorenko
Publisher : Springer Science & Business Media
Page : 268 pages
File Size : 44,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401588973

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Dynamics of One-Dimensional Maps by A.N. Sharkovsky,S.F. Kolyada,A.G. Sivak,V.V. Fedorenko Pdf

maps whose topological entropy is equal to zero (i.e., maps that have only cyeles of pe 2 riods 1,2,2 , ... ) are studied in detail and elassified. Various topological aspects of the dynamics of unimodal maps are studied in Chap ter 5. We analyze the distinctive features of the limiting behavior of trajectories of smooth maps. In particular, for some elasses of smooth maps, we establish theorems on the number of sinks and study the problem of existence of wandering intervals. In Chapter 6, for a broad elass of maps, we prove that almost all points (with respect to the Lebesgue measure) are attracted by the same sink. Our attention is mainly focused on the problem of existence of an invariant measure absolutely continuous with respect to the Lebesgue measure. We also study the problem of Lyapunov stability of dynamical systems and determine the measures of repelling and attracting invariant sets. The problem of stability of separate trajectories under perturbations of maps and the problem of structural stability of dynamical systems as a whole are discussed in Chap ter 7. In Chapter 8, we study one-parameter families of maps. We analyze bifurcations of periodic trajectories and properties of the set of bifurcation values of the parameter, in eluding universal properties such as Feigenbaum universality.

Author : Araceli Bonifant,Misha Lyubich,Scott Sutherland
Publisher : Princeton University Press
Page : 799 pages
File Size : 41,6 Mb
Release : 2014-03-16
Category : Mathematics
ISBN : 9780691159294

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Frontiers in Complex Dynamics by Araceli Bonifant,Misha Lyubich,Scott Sutherland Pdf

John Milnor, best known for his work in differential topology, K-theory, and dynamical systems, is one of only three mathematicians to have won the Fields medal, the Abel prize, and the Wolf prize, and is the only one to have received all three of the Leroy P. Steele prizes. In honor of his eightieth birthday, this book gathers together surveys and papers inspired by Milnor's work, from distinguished experts examining not only holomorphic dynamics in one and several variables, but also differential geometry, entropy theory, and combinatorial group theory. The book contains the last paper written by William Thurston, as well as a short paper by John Milnor himself. Introductory sections put the papers in mathematical and historical perspective, color figures are included, and an index facilitates browsing. This collection will be useful to students and researchers for decades to come. The contributors are Marco Abate, Marco Arizzi, Alexander Blokh, Thierry Bousch, Xavier Buff, Serge Cantat, Tao Chen, Robert Devaney, Alexandre Dezotti, Tien-Cuong Dinh, Romain Dujardin, Hugo García-Compeán, William Goldman, Rotislav Grigorchuk, John Hubbard, Yunping Jiang, Linda Keen, Jan Kiwi, Genadi Levin, Daniel Meyer, John Milnor, Carlos Moreira, Vincente Muñoz, Viet-Anh Nguyên, Lex Oversteegen, Ricardo Pérez-Marco, Ross Ptacek, Jasmin Raissy, Pascale Roesch, Roberto Santos-Silva, Dierk Schleicher, Nessim Sibony, Daniel Smania, Tan Lei, William Thurston, Vladlen Timorin, Sebastian van Strien, and Alberto Verjovsky.

Author : Pascal Chossat,Reiner Lauterbach
Publisher : World Scientific Publishing Company
Page : 420 pages
File Size : 48,8 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.

Author : B. Hasselblatt,A. Katok
Publisher : Elsevier
Page : 1232 pages
File Size : 50,5 Mb
Release : 2002-08-20
Category : Mathematics
ISBN : 9780080533445

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Handbook of Dynamical Systems by B. Hasselblatt,A. Katok Pdf

Volumes 1A and 1B. These volumes give a comprehensive survey of dynamics written by specialists in the various subfields of dynamical systems. The presentation attains coherence through a major introductory survey by the editors that organizes the entire subject, and by ample cross-references between individual surveys. The volumes are a valuable resource for dynamicists seeking to acquaint themselves with other specialties in the field, and to mathematicians active in other branches of mathematics who wish to learn about contemporary ideas and results dynamics. Assuming only general mathematical knowledge the surveys lead the reader towards the current state of research in dynamics. Volume 1B will appear 2005.

Author : Andreas Galka
Publisher : World Scientific
Page : 368 pages
File Size : 46,6 Mb
Release : 2000
Category : Mathematics
ISBN : 9810241488

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Topics in Nonlinear Time Series Analysis by Andreas Galka Pdf

This book provides a thorough review of a class of powerful algorithms for the numerical analysis of complex time series data which were obtained from dynamical systems. These algorithms are based on the concept of state space representations of the underlying dynamics, as introduced by nonlinear dynamics. In particular, current algorithms for state space reconstruction, correlation dimension estimation, testing for determinism and surrogate data testing are presented ? algorithms which have been playing a central role in the investigation of deterministic chaos and related phenomena since 1980. Special emphasis is given to the much-disputed issue whether these algorithms can be successfully employed for the analysis of the human electroencephalogram.

Author : Viviane Baladi
Publisher : World Scientific
Page : 326 pages
File Size : 50,7 Mb
Release : 2000-07-12
Category : Science
ISBN : 9789814496667

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Positive Transfer Operators And Decay Of Correlations by Viviane Baladi Pdf

Although individual orbits of chaotic dynamical systems are by definition unpredictable, the average behavior of typical trajectories can often be given a precise statistical description. Indeed, there often exist ergodic invariant measures with special additional features. For a given invariant measure, and a class of observables, the correlation functions tell whether (and how fast) the system “mixes”, i.e. “forgets” its initial conditions.This book, addressed to mathematicians and mathematical (or mathematically inclined) physicists, shows how the powerful technology of transfer operators, imported from statistical physics, has been used recently to construct relevant invariant measures, and to study the speed of decay of their correlation functions, for many chaotic systems. Links with dynamical zeta functions are explained.The book is intended for graduate students or researchers entering the field, and the technical prerequisites have been kept to a minimum.

Author : Jan Awrejcewicz
Publisher : Springer
Page : 413 pages
File Size : 55,8 Mb
Release : 2018-09-01
Category : Mathematics
ISBN : 9783319965987

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Dynamical Systems in Theoretical Perspective by Jan Awrejcewicz Pdf

This book focuses on theoretical aspects of dynamical systems in the broadest sense. It highlights novel and relevant results on mathematical and numerical problems that can be found in the fields of applied mathematics, physics, mechanics, engineering and the life sciences. The book consists of contributed research chapters addressing a diverse range of problems. The issues discussed include (among others): numerical-analytical algorithms for nonlinear optimal control problems on a large time interval; gravity waves in a reservoir with an uneven bottom; value distribution and growth of solutions for certain Painlevé equations; optimal control of hybrid systems with sliding modes; a mathematical model of the two types of atrioventricular nodal reentrant tachycardia; non-conservative instability of cantilevered nanotubes using the Cell Discretization Method; dynamic analysis of a compliant tensegrity structure for use in a gripper application; and Jeffcott rotor bifurcation behavior using various models of hydrodynamic bearings.

Author : Christopher Keil McCord
Publisher : American Mathematical Soc.
Page : 350 pages
File Size : 52,5 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821851814

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Nielsen Theory and Dynamical Systems by Christopher Keil McCord Pdf

This volume contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Nielsen Theory and Dynamical Systems, held in June 1992 at Mount Holyoke College. Focusing on the interface between Nielsen fixed point theory and dynamical systems, this book provides an almost complete survey of the state of the art of Nielsen theory. Most of the articles are expository, making them accessible to both graduate students and researchers in algebraic topology, fixed point theory, and dynamical systems.

Author : Yunping Jiang
Publisher : World Scientific
Page : 327 pages
File Size : 40,6 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.