Combinatorial Dynamics And Entropy In Dimension One (2nd Edition)
Title | Combinatorial Dynamics And Entropy In Dimension One (2nd Edition) PDF eBook |
Author | Luis Alseda |
Publisher | World Scientific Publishing Company |
Pages | 433 |
Release | 2000-10-31 |
Genre | Science |
ISBN | 9813105593 |
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.
Combinatorial Dynamics and Entropy in Dimension One
Title | Combinatorial Dynamics and Entropy in Dimension One PDF eBook |
Author | Ll Alsedà |
Publisher | World Scientific Publishing Company Incorporated |
Pages | 415 |
Release | 2000 |
Genre | Mathematics |
ISBN | 9789810240530 |
This book introduces the reader to two of the main directions of one-dimensional dynamics. The first has its roots in the Sharkovskii theorem, which describes the possible sets of periods of all 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. A good way of doing this is to study the topological entropy of the system. The aim of this book is to provide graduate students and researchers with a unified and detailed exposition of these developments for interval and circle maps. The second edition contains two new appendices, where an extension of the theory to tree and graph maps is presented without technical proofs.
Combinatorial Dynamics and Entropy in Dimension One
Title | Combinatorial Dynamics and Entropy in Dimension One PDF eBook |
Author | Ll Alsedà |
Publisher | |
Pages | |
Release | 2000 |
Genre | |
ISBN | 9789812813367 |
Methods In Equivariant Bifurcations And Dynamical Systems
Title | Methods In Equivariant Bifurcations And Dynamical Systems PDF eBook |
Author | Pascal Chossat |
Publisher | World Scientific Publishing Company |
Pages | 422 |
Release | 2000-02-28 |
Genre | Science |
ISBN | 9813105445 |
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.
Topics in Nonlinear Time Series Analysis
Title | Topics in Nonlinear Time Series Analysis PDF eBook |
Author | Andreas Galka |
Publisher | World Scientific |
Pages | 368 |
Release | 2000 |
Genre | Mathematics |
ISBN | 9789810241483 |
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.
Positive Transfer Operators And Decay Of Correlations
Title | Positive Transfer Operators And Decay Of Correlations PDF eBook |
Author | Viviane Baladi |
Publisher | World Scientific |
Pages | 326 |
Release | 2000-07-12 |
Genre | Science |
ISBN | 9814496669 |
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.
Encyclopedia of Nonlinear Science
Title | Encyclopedia of Nonlinear Science PDF eBook |
Author | Alwyn Scott |
Publisher | Routledge |
Pages | 1107 |
Release | 2006-05-17 |
Genre | Reference |
ISBN | 1135455589 |
In 438 alphabetically-arranged essays, this work provides a useful overview of the core mathematical background for nonlinear science, as well as its applications to key problems in ecology and biological systems, chemical reaction-diffusion problems, geophysics, economics, electrical and mechanical oscillations in engineering systems, lasers and nonlinear optics, fluid mechanics and turbulence, and condensed matter physics, among others.