Dynamical Systems, Graphs, and Algorithms

2007
ISBN: 978-3-540-35593-9
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1889, 288 Seiten, Book w. online files / update, Format (B × H): 155 mm x 235 mm, Gewicht: 464 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Osipenko, George

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

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.