Dynamical systems, graphs, and algorithms

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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)

Author(s): Prof. George Osipenko (auth.)
Series: Lecture Notes in Mathematics 1889
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2007

Language: English
Pages: 288
City: Berlin ; New York
Tags: Global Analysis and Analysis on Manifolds; Numerical Analysis; Ordinary Differential Equations

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