One Dimensional Dynamics
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One Dimensional Dynamics
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Author : Welington de Melo
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
One Dimensional Dynamics written by Welington de Melo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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).
Topics From One Dimensional Dynamics
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Author : Karen M. Brucks
language : en
Publisher: Cambridge University Press
Release Date : 2004-06-28
Topics From One Dimensional Dynamics written by Karen M. Brucks and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-28 with Mathematics categories.
One-dimensional dynamics owns many deep results and avenues of active mathematical research. Numerous inroads to this research exist for the advanced undergraduate or beginning graduate student. This book provides glimpses into one-dimensional dynamics with the hope that the results presented illuminate the beauty and excitement of the field. Much of this material is covered nowhere else in textbook format, some are mini new research topics in themselves, and novel connections are drawn with other research areas both inside and outside the text. The material presented here is not meant to be approached in a linear fashion. Readers are encouraged to pick and choose favourite topics. Anyone with an interest in dynamics, novice or expert alike, will find much of interest within.
Dynamics Of One Dimensional Maps
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Author : A.N. Sharkovsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Dynamics Of One Dimensional Maps written by A.N. Sharkovsky and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
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.
Dynamics In One Dimension
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Author : Louis S. Block
language : en
Publisher: Springer
Release Date : 2006-11-14
Dynamics In One Dimension written by Louis S. Block and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
The behaviour under iteration of unimodal maps of an interval, such as the logistic map, has recently attracted considerable attention. It is not so widely known that a substantial theory has by now been built up for arbitrary continuous maps of an interval. The purpose of the book is to give a clear account of this subject, with complete proofs of many strong, general properties. In a number of cases these have previously been difficult of access. The analogous theory for maps of a circle is also surveyed. Although most of the results were unknown thirty years ago, the book will be intelligible to anyone who has mastered a first course in real analysis. Thus the book will be of use not only to students and researchers, but will also provide mathematicians generally with an understanding of how simple systems can exhibit chaotic behaviour.
One Dimensional Dynamics
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Author : Welington de Melo
language : en
Publisher: Springer
Release Date : 1993-08-17
One Dimensional Dynamics written by Welington de Melo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-08-17 with Mathematics categories.
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).
One Dimensional Dynamical Systems
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Author : Ana Rodrigues
language : en
Publisher: Chapman & Hall/CRC
Release Date : 2021
One Dimensional Dynamical Systems written by Ana Rodrigues and has been published by Chapman & Hall/CRC this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Mathematics categories.
For almost every phenomenon in Physics, Chemistry, Biology, Medicine, Economics, and other sciences one can make a mathematical model that can be regarded as a dynamical system. One-Dimensional Dynamical Systems: An Example-Led Approach seeks to deep-dive into α standard maps as an example-driven way of explaining the modern theory of the subject in a way that will be engaging for students. Features Example-driven approach Suitable as supplementary reading for a graduate or advanced undergraduate course in dynamical systems.
Dynamics Of One Dimensional Quantum Systems
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Author : Yoshio Kuramoto
language : en
Publisher: Cambridge University Press
Release Date : 2009-08-06
Dynamics Of One Dimensional Quantum Systems written by Yoshio Kuramoto and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-06 with Mathematics categories.
A concise and accessible account of the dynamical properties of one-dimensional quantum systems, for graduate students and new researchers.
Non Equilibrium Dynamics Of One Dimensional Bose Gases
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Author : Tim Langen
language : en
Publisher: Springer
Release Date : 2015-05-22
Non Equilibrium Dynamics Of One Dimensional Bose Gases written by Tim Langen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-22 with Science categories.
This work presents a series of experiments with ultracold one-dimensional Bose gases, which establish said gases as an ideal model system for exploring a wide range of non-equilibrium phenomena. With the help of newly developed tools, like full distributions functions and phase correlation functions, the book reveals the emergence of thermal-like transient states, the light-cone-like emergence of thermal correlations and the observation of generalized thermodynamic ensembles. This points to a natural emergence of classical statistical properties from the microscopic unitary quantum evolution, and lays the groundwork for a universal framework of non-equilibrium physics. The thesis investigates a central question that is highly contested in quantum physics: how and to which extent does an isolated quantum many-body system relax? This question arises in many diverse areas of physics, and many of the open problems appear at vastly different energy, time and length scales, ranging from high-energy physics and cosmology to condensed matter and quantum information. A key challenge in attempting to answer this question is the scarcity of quantum many-body systems that are both well isolated from the environment and accessible for experimental study.
An Introduction To Chaotic Dynamical Systems
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Author : Robert Devaney
language : en
Publisher: CRC Press
Release Date : 2018-03-09
An Introduction To Chaotic Dynamical Systems written by Robert Devaney and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-09 with Mathematics categories.
The study of nonlinear dynamical systems has exploded in the past 25 years, and Robert L. Devaney has made these advanced research developments accessible to undergraduate and graduate mathematics students as well as researchers in other disciplines with the introduction of this widely praised book. In this second edition of his best-selling text, Devaney includes new material on the orbit diagram fro maps of the interval and the Mandelbrot set, as well as striking color photos illustrating both Julia and Mandelbrot sets. This book assumes no prior acquaintance with advanced mathematical topics such as measure theory, topology, and differential geometry. Assuming only a knowledge of calculus, Devaney introduces many of the basic concepts of modern dynamical systems theory and leads the reader to the point of current research in several areas.
Chaos On The Interval
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Author : Sylvie Ruette
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-03-02
Chaos On The Interval written by Sylvie Ruette and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-02 with Mathematics categories.
The aim of this book is to survey the relations between the various kinds of chaos and related notions for continuous interval maps from a topological point of view. The papers on this topic are numerous and widely scattered in the literature; some of them are little known, difficult to find, or originally published in Russian, Ukrainian, or Chinese. Dynamical systems given by the iteration of a continuous map on an interval have been broadly studied because they are simple but nevertheless exhibit complex behaviors. They also allow numerical simulations, which enabled the discovery of some chaotic phenomena. Moreover, the “most interesting” part of some higher-dimensional systems can be of lower dimension, which allows, in some cases, boiling it down to systems in dimension one. Some of the more recent developments such as distributional chaos, the relation between entropy and Li-Yorke chaos, sequence entropy, and maps with infinitely many branches are presented in book form for the first time. The author gives complete proofs and addresses both graduate students and researchers.