Dynamical systems, graphs, and algorithms
Author(s)
Bibliographic Information
Dynamical systems, graphs, and algorithms
（Lecture notes in mathematics, 1889）
Springer, c2007
Available at / 62 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
L/N||LNM||188906061147
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Note
Includes bibliographical references and index
Description and Table of Contents
Description
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.
Table of 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.
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