Complex Dynamics And Renormalization

Author : Yunping Jiang
Publisher : World Scientific
Page : 327 pages
File Size : 48,9 Mb
Release : 1996-09-20
Category : Science
ISBN : 9789814500173

Get Book

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.

Author : Curtis T. McMullen
Publisher : Princeton University Press
Page : 228 pages
File Size : 45,6 Mb
Release : 1994-12-19
Category : Mathematics
ISBN : 0691029814

Get Book

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.

Author : Mikhail Lyubich,Michael Yampolsky
Publisher : American Mathematical Soc.
Page : 408 pages
File Size : 44,7 Mb
Release : 2008
Category : Hamiltonian systems
ISBN : 9780821842751

Get Book

Holomorphic Dynamics and Renormalization by Mikhail Lyubich,Michael Yampolsky Pdf

Collects papers that reflect some of the directions of research in two closely related fields: Complex Dynamics and Renormalization in Dynamical Systems. This title contains papers that introduces the reader to this fascinating world and a related area of transcendental dynamics. It also includes open problems and computer simulations.

Author : Curtis T. McMullen
Publisher : Princeton University Press
Page : 264 pages
File Size : 48,5 Mb
Release : 2014-09-08
Category : Mathematics
ISBN : 9781400865178

Get Book

Renormalization and 3-Manifolds Which Fiber over the Circle (AM-142), Volume 142 by Curtis T. McMullen Pdf

Many parallels between complex dynamics and hyperbolic geometry have emerged in the past decade. Building on work of Sullivan and Thurston, this book gives a unified treatment of the construction of fixed-points for renormalization and the construction of hyperbolic 3- manifolds fibering over the circle. Both subjects are studied via geometric limits and rigidity. This approach shows open hyperbolic manifolds are inflexible, and yields quantitative counterparts to Mostow rigidity. In complex dynamics, it motivates the construction of towers of quadratic-like maps, and leads to a quantitative proof of convergence of renormalization.

Author : Yunping Jiang
Publisher : World Scientific
Page : 344 pages
File Size : 41,6 Mb
Release : 1996
Category : Science
ISBN : 9810223269

Get Book

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.

Author : Dierk Schleicher
Publisher : CRC Press
Page : 663 pages
File Size : 48,7 Mb
Release : 2009-11-03
Category : Mathematics
ISBN : 9781439865422

Get Book

Complex Dynamics by Dierk Schleicher Pdf

Complex Dynamics: Families and Friends features contributions by many of the leading mathematicians in the field, such as Mikhail Lyubich, John Milnor, Mitsuhiro Shishikura, and William Thurston. Some of the chapters, including an introduction by Thurston to the general subject of complex dynamics, are classic manuscripts that were never published

Author : Yaneer Bar-yam
Publisher : CRC Press
Page : 866 pages
File Size : 46,9 Mb
Release : 2019-03-04
Category : Mathematics
ISBN : 9780429717598

Get Book

Dynamics Of Complex Systems by Yaneer Bar-yam Pdf

This book aims to develop models and modeling techniques that are useful when applied to all complex systems. It adopts both analytic tools and computer simulation. The book is intended for students and researchers with a variety of backgrounds.

Author : Araceli Bonifant,Misha Lyubich,Scott Sutherland
Publisher : Princeton University Press
Page : 824 pages
File Size : 45,9 Mb
Release : 2014-03-16
Category : Mathematics
ISBN : 9781400851317

Get Book

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 : Saeed Zakeri
Publisher : Springer
Page : 124 pages
File Size : 41,9 Mb
Release : 2018-06-23
Category : Mathematics
ISBN : 9783319788104

Get Book

Rotation Sets and Complex Dynamics by Saeed Zakeri Pdf

This monograph examines rotation sets under the multiplication by d (mod 1) map and their relation to degree d polynomial maps of the complex plane. These sets are higher-degree analogs of the corresponding sets under the angle-doubling map of the circle, which played a key role in Douady and Hubbard's work on the quadratic family and the Mandelbrot set. Presenting the first systematic study of rotation sets, treating both rational and irrational cases in a unified fashion, the text includes several new results on their structure, their gap dynamics, maximal and minimal sets, rigidity, and continuous dependence on parameters. This abstract material is supplemented by concrete examples which explain how rotation sets arise in the dynamical plane of complex polynomial maps and how suitable parameter spaces of such polynomials provide a complete catalog of all such sets of a given degree. As a main illustration, the link between rotation sets of degree 3 and one-dimensional families of cubic polynomials with a persistent indifferent fixed point is outlined. The monograph will benefit graduate students as well as researchers in the area of holomorphic dynamics and related fields.

Author : Anonim
Publisher : Unknown
Page : 395 pages
File Size : 41,8 Mb
Release : 2008
Category : Hamiltonian systems
ISBN : 1470430878

Get Book

Holomorphic Dynamics and Renormalization by Anonim Pdf

The papers collected in this volume reflect some of the directions of research in two closely related fields: Complex Dynamics and Renormalization in Dynamical Systems. While dynamics of polynomial mappings, particularly quadratics, has by now reached a mature state of development, much less is known about non-polynomial rational maps. The reader will be introduced into this fascinating world and a related area of transcendental dynamics by the papers in this volume. A graduate student will find an area rich with open problems and beautiful computer simulations. A survey by V. Nekrashevych int.

Author : David P. Feldman
Publisher : Princeton University Press
Page : 262 pages
File Size : 44,6 Mb
Release : 2019-08-06
Category : Mathematics
ISBN : 9780691161525

Get Book

Chaos and Dynamical Systems by David P. Feldman Pdf

Chaos and Dynamical Systems presents an accessible, clear introduction to dynamical systems and chaos theory, important and exciting areas that have shaped many scientific fields. While the rules governing dynamical systems are well-specified and simple, the behavior of many dynamical systems is remarkably complex. Of particular note, simple deterministic dynamical systems produce output that appears random and for which long-term prediction is impossible. Using little math beyond basic algebra, David Feldman gives readers a grounded, concrete, and concise overview. In initial chapters, Feldman introduces iterated functions and differential equations. He then surveys the key concepts and results to emerge from dynamical systems: chaos and the butterfly effect, deterministic randomness, bifurcations, universality, phase space, and strange attractors. Throughout, Feldman examines possible scientific implications of these phenomena for the study of complex systems, highlighting the relationships between simplicity and complexity, order and disorder. Filling the gap between popular accounts of dynamical systems and chaos and textbooks aimed at physicists and mathematicians, Chaos and Dynamical Systems will be highly useful not only to students at the undergraduate and advanced levels, but also to researchers in the natural, social, and biological sciences.

Author : B. Branner,Poul Hjorth
Publisher : Springer Science & Business Media
Page : 354 pages
File Size : 47,8 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9789401584395

Get Book

Real and Complex Dynamical Systems by B. Branner,Poul Hjorth Pdf

This volume contains edited versions of 11 contributions given by main speakers at the NATO Advanced Study Institute on lReal and Complex Dynamical Systems in Hiller0d, Denmark, June 20th - July 2nd, 1993. The vision of the institute was to illustrate the interplay between two important fields of Mathematics: Real Dynamical Systems and Complex Dynamical Systems. The interaction between these two fields has been growing over the years. Problems in Real Dynamical Systems have recently been solved using complex tools in the real or by extension to the complex. In return, problems in Complex Dynamical Systems have been settled using results from Real Dynamical Systems. The programme of the institute was to examine the state of the art of central parts of both Real and Complex Dynamical Systems, to reinforce contact between the two aspects of the theory and to make recent progress in each accessible to a larger group of mathematicians.

Author : Kevin M. Pilgrim
Publisher : Springer Science & Business Media
Page : 132 pages
File Size : 44,9 Mb
Release : 2003
Category : Differentiable dynamical systems
ISBN : 3540201734

Get Book

Combinations of Complex Dynamical Systems by Kevin M. Pilgrim Pdf

Author : Israel Michael Sigal,Catherine Sulem
Publisher : American Mathematical Soc.
Page : 202 pages
File Size : 48,7 Mb
Release : 2001
Category : Differential equations, Nonlinear
ISBN : 9780821828021

Get Book

Nonlinear Dynamics and Renormalization Group by Israel Michael Sigal,Catherine Sulem Pdf

This book contains the proceedings from the workshop, Nonlinear Dynamics and Renormalization Group, held at the Centre de recherches mathématiques (CRM) in Montréal (Canada), as part of the year-long program devoted to mathematical physics. In the book, active researchers in the fields of nonlinear partial differential equations and renormalization group contribute recent results on topics such as Ginzburg-Landau equations and blow-up of solutions of the nonlinear Schroedinger equations, quantum resonances, and renormalization group analysis in constructive quantum field theory. This volume offers the latest research in the rapidly developing fields of nonlinear equations and renormalization group.

Author : Steven H. Strogatz
Publisher : CRC Press
Page : 532 pages
File Size : 41,7 Mb
Release : 2018-05-04
Category : Mathematics
ISBN : 9780429961113

Get Book

Nonlinear Dynamics and Chaos by Steven H. Strogatz Pdf

This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.