Mathematics-Dynamical Systems

Dynamical systems, graphs, and algorithms

US$5.00 US$39.00

Title (user) : Dynamical systems, graphs, and algorithmsISBN : 9783540355939,3540355936ISSN : 0075-8434DOI : 10.1007/3-540-35593-6GoogleBook ID : rF8rAAAAYAAJOpenLibrary ID : OL9056629MEdition : 1Series : Lecture notes in mathematics 1889Authors...
Description

Title (user) : Dynamical systems, graphs, and algorithms

ISBN : 9783540355939,3540355936

ISSN : 0075-8434

DOI : 10.1007/3-540-35593-6

GoogleBook ID : rF8rAAAAYAAJ

OpenLibrary ID : OL9056629M

Edition : 1

Series : Lecture notes in mathematics 1889

Authors (user) : Prof. George Osipenko (auth.)

Authors (google) : George Osipenko

Publisher : Springer-Verlag Berlin Heidelberg

Language : English

Publication Date : 2007

Scanned : yes (300 DPI)

File Format : djvu

Categories : Mathematics


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Description (user) :

From the reviews:

"This book provides a taster for using symbolic analysis, graph theory, and set-oriented methods in a quest to understand the global structure of the dynamics in a continuous- or discrete-time system. In many ways, the techniques discussed here are complementary to more traditional ways of analysing a dynamical system and as such, this book can be viewed as a valuable entry into the theory and computational methods. … The book is intended for postgraduate researchers … ." (Hinke M. Osinga, Mathematical Reviews, Issue 2008 i)

"This monograph contains a summary of the author’s work on constructive methods for the study of discrete dynamical systems. … The structure of the book is very clear with 14 chapters devoted to different dynamical objects such as chain recurrent sets, structural stability or invariant manifolds, followed by two examples: the Ikeda mapping and a discrete food-chain model. … is certainly a valuable and very readable reference, in particular for the study of low-dimensional concrete systems with complicated dynamics." (Jörg Härterich, Zentralblatt MATH, Vol. 1130 (8), 2008)


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Description (google) :
This book describes a family of algorithms for studying the global structure of systems. By a finite covering of the phase space we construct a directed graph with vertices corresponding to cells of the covering and edges corresponding to admissible transitions. The method is used, among other things, to locate the periodic orbits and the chain recurrent set, to construct the attractors and their basins, to estimate the entropy, and more.


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Table of contents :
Front Matter....Pages I-XII
Introduction....Pages 1-14
Symbolic Image....Pages 15-25
Periodic Trajectories....Pages 27-33
Newton's Method....Pages 35-41
Invariant Sets....Pages 43-54
Chain Recurrent Set....Pages 55-63
Attractors....Pages 65-83
Filtration....Pages 85-95
Structural Graph....Pages 97-105
Entropy....Pages 107-121
Projective Space and Lyapunov Exponents....Pages 123-136
Morse Spectrum....Pages 137-160
Hyperbolicity and Structural Stability....Pages 161-174
Controllability....Pages 175-179
Invariant Manifolds....Pages 181-195
Ikeda Mapping Dynamics....Pages 197-218
A Dynamical System of Mathematical Biology....Pages 219-232
Back Matter....Pages 233-287

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