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Grammatical Complexity and One-dimensional Dynamical Systems

Author: Huimin Xie

Publisher: World Scientific

Published: 1996

Total Pages: 290

ISBN-13: 9810223986

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Grammatical Complexity and One-Dimensional Dynamical Systems

Author: H-M Xie

Publisher: World Scientific

Published: 1996-11-23

Total Pages: 288

ISBN-13: 9814499897

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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. Contents:Strings and Languages:Free MonoidsDynamical LanguagesGrammatical Complexity of Unimodal Maps:Languages of Unimodal MapsRegular Languages of Unimodal MapsA General Discussion of Kneading SequencesNon-Regular Languages of Unimodal MapsDEB of Unimodal MapsTopological Entropy of Unimodal MapsGrammatical Complexity of Circle Homeomorphisms:Languages of Circle HomeomorphismsComplexity Levels of Circle HomeomorphismsAutomata of Circle HomeomorphismsAppendices:Finite Automata and Regular LanguagesNon-Regular LanguagesL Systems and Languages Readership:Scientists interested in chaos and nonlinear science. keywords:Grammatical Complexity;Dynamical Systems;Symbolic Dynamics;Unimodal Maps;Circle Homeomorphisms;Kneading Sequences;Formal Languages;Chomsky Hierarchy;L Systems;Distinct Excluded Blocks;Topological Entropy

Reviews of Nonlinear Dynamics and Complexity

Author: Heinz Georg Schuster

Publisher: John Wiley & Sons

Published: 2009-09-03

Total Pages: 227

ISBN-13: 3527626360

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Adopting a cross-disciplinary approach, the review character of this monograph sets it apart from specialized journals. The editor is advised by a first-class board of international scientists, such that the carefully selected and invited contributions represent the latest and most relevant findings. The resulting review enables both researchers and newcomers in life science, physics, and chemistry to access the most important results in this field, using a common language.

Lozi Mappings

Author: Zeraoulia Elhadj

Publisher: CRC Press

Published: 2013-08-17

Total Pages: 334

ISBN-13: 1466580720

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This book is a comprehensive collection of known results about the Lozi map, a piecewise-affine version of the Henon map. Henon map is one of the most studied examples in dynamical systems and it attracts a lot of attention from researchers, however it is difficult to analyze analytically. Simpler structure of the Lozi map makes it more suitable fo

Topological and Ergodic Theory of Symbolic Dynamics

Author: Henk Bruin

Publisher: American Mathematical Society

Published: 2022-12-21

Total Pages: 481

ISBN-13: 1470472198

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Symbolic dynamics is essential in the study of dynamical systems of various types and is connected to many other fields such as stochastic processes, ergodic theory, representation of numbers, information and coding, etc. This graduate text introduces symbolic dynamics from a perspective of topological dynamical systems and presents a vast variety of important examples. After introducing symbolic and topological dynamics, the core of the book consists of discussions of various subshifts of positive entropy, of zero entropy, other non-shift minimal action on the Cantor set, and a study of the ergodic properties of these systems. The author presents recent developments such as spacing shifts, square-free shifts, density shifts, $mathcal{B}$-free shifts, Bratteli-Vershik systems, enumeration scales, amorphic complexity, and a modern and complete treatment of kneading theory. Later, he provides an overview of automata and linguistic complexity (Chomsky's hierarchy). The necessary background for the book varies, but for most of it a solid knowledge of real analysis and linear algebra and first courses in probability and measure theory, metric spaces, number theory, topology, and set theory suffice. Most of the exercises have solutions in the back of the book.

Applied Symbolic Dynamics And Chaos

Author: Bailin Hao

Publisher: World Scientific

Published: 1998-07-04

Total Pages: 460

ISBN-13: 9814495972

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Latest Edition: Applied Symbolic Dynamics and Chaos (2nd Edition)Symbolic dynamics is a coarse-grained description of dynamics. It provides a rigorous way to understand the global systematics of periodic and chaotic motion in a system. In the last decade it has been applied to nonlinear systems described by one- and two-dimensional maps as well as by ordinary differential equations. This book will help practitioners in nonlinear science and engineering to master that powerful tool.

Applied Symbolic Dynamics And Chaos (Second Edition)

Author: Hao Bailin

Publisher: World Scientific

Published: 2018-05-11

Total Pages: 520

ISBN-13: 9813236442

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Symbolic dynamics is a coarse-grained description of dynamics. It has been a long-studied chapter of the mathematical theory of dynamical systems, but its abstract formulation has kept many practitioners of physical sciences and engineering from appreciating its simplicity, beauty, and power. At the same time, symbolic dynamics provides almost the only rigorous way to understand global systematics of periodic and, especially, chaotic motion in dynamical systems. In a sense, everyone who enters the field of chaotic dynamics should begin with the study of symbolic dynamics. However, this has not been an easy task for non-mathematicians. On one hand, the method of symbolic dynamics has been developed to such an extent that it may well become a practical tool in studying chaotic dynamics, both on computers and in laboratories. On the other hand, most of the existing literature on symbolic dynamics is mathematics-oriented. This book is an attempt at partially filling up this apparent gap by emphasizing the applied aspects of symbolic dynamics without mathematical rigor. Contents: Preface to the Second Edition Preface to the First Edition Introduction Symbolic Dynamics of Unimodal Maps Maps with Multiple Critical Points Symbolic Dynamics of Circle Maps Symbolic Dynamics of Two-Dimensional Maps Application to Ordinary Differential Equations Counting the Number of Periodic Orbits Symbolic Dynamics and Grammatical Complexity Symbolic Dynamics and Knot Theory Appendix References Index Readership: Researchers and students interested in chaotic dynamics. Keywords: Symbolic Dynamics;ChaosReview: Key Features: No previous knowledge of dynamical systems theory is required in order to read this book The revisions concern mainly the application to ordinary differential equations via constructing two-dimensional symbolic dynamics of the corresponding Poincare maps

Yang-baxter Systems, Nonlinear Models And Their Applications - Proceedings Of The Apctp-nankai Symposium

Author: B K Chung

Publisher: World Scientific

Published: 1999-12-13

Total Pages: 206

ISBN-13: 9814543241

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Machines, Computations, and Universality

Author: Jérôme Durand-Lose

Publisher: Springer

Published: 2018-06-04

Total Pages: 171

ISBN-13: 3319924028

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This book constitutes the refereed proceedings of the 8th International Conference on Machines, Computations, and Universality, MCU 2018, held in Fontainebleau, France, in June 2018. The 9 revised full papers presented together with 5 invited talks were carefully reviewed and selected from numerous submissions. MCU explores computation in the setting of various discrete models (Turing machines, register machines, cellular automata, tile assembly systems, rewriting systems, molecular computing models, neural models, concurrent systems, etc.) and analog and hybrid models (BSS machines, infinite time cellular automata, real machines, quantum computing, etc.).

Applied Symbolic Dynamics and Chaos

Author: Bai-lin Hao

Publisher: World Scientific

Published: 1998

Total Pages: 468

ISBN-13: 9789810235123

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Symbolic dynamics is a coarse-grained description of dynamics. It provides a rigorous way to understand the global systematics of periodic and chaotic motion in a system. In the last decade it has been applied to nonlinear systems described by one- and two-dimensional maps as well as by ordinary differential equations. This book will help practitioners in nonlinear science and engineering to master that powerful tool.