Description 
1 online resource (xii, 283 pages) : illustrations 
Series 
Lecture notes in mathematics, 00758434 ; 1889 

Lecture notes in mathematics (SpringerVerlag) ; 1889

Contents 
Symbolic image  Periodic trajectories  Newton's method  Invariant sets  Chain recurrent set  Attractors  Filtration  Structural graph  Entropy  Projective space and Lyapunov exponents  Morse spectrum  Hyperbolicity and structural stability  Controllability  Invariant manifolds  Ikeda mapping dynamics  A dynamical system of mathematical biology  [Appendix] A. Double logistic map  [Appendix] B. Implementation of the symbolic image 
Summary 
The modern theory and practice of dynamical systems requires the study of structures that fall outside the scope of traditional subjects of mathematical analysis. An important tool to investigate such complicated phenomena as chaos and strange attractors is the method of symbolic dynamics. This book describes a family of the algorithms to study global structure of systems. By a finite covering of the phase space we construct a directed graph (symbolic image) with vertices corresponding to cells of the covering and edges corresponding to admissible transitions. The method is used to localize the periodic orbits and the chain recurrent set, to construct the attractors and their basins, to estimate the entropy, Lyapunov exponents and the Morse spectrum, to verify the hyperbolicity and the structural stability. Considerable information can be obtained thus, and more techniques may be discovered in future research 
Bibliography 
Includes bibliographical references and index 
Notes 
Print version record 
Subject 
Symbolic dynamics.


Topological dynamics.


Differentiable dynamical systems.

Form 
Electronic book

LC no. 
2006930097 
ISBN 
1280700300 

3540355936 

3540355952 

6610700303 

9781280700309 

9783540355939 

9783540355953 

9786610700301 
