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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.
The W₃ algebra: modules, semi-infinite cohomology, and BV algebras Автор: Peter Bouwknegt Год: 1996 |
Dynamical Systems Graphs and Algorithms Автор: George Osipenko Год: 2006 |
The W3 Algebra: Modules, Semi-infinite Cohomology and BV Algebras (Lecture Notes in Physics Monographs) Автор: Peter Bouwknegt, Jim McCarthy, Krzysztof Pilch Год: 1996 |
Dynamical Systems, Graphs, and Algorithms (Lecture Notes in Mathematics) Автор: George Osipenko Год: 2006 |
Brocard Triangle Год: 2011 |
Multiphase Flows in Small Scale Pipes Автор: Wegmann A. Год: 2005 |