Dynamical systems, graphs, and algorithms /
Osipenko, George.
Dynamical systems, graphs, and algorithms / George Osipenko. - Berlin ; New York : Springer, ©2007. - 1 online resource (xii, 283 pages) : illustrations - Lecture notes in mathematics, 1889 0075-8434 ; . - Lecture notes in mathematics (Springer-Verlag) ; 1889. .
Includes bibliographical references and index.
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 -- [Appendix] A. Double logistic map -- [Appendix] B. Implementation of the symbolic image.
Use copy
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.
Electronic reproduction.
[Place of publication not identified] :
HathiTrust Digital Library,
2010.
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
http://purl.oclc.org/DLF/benchrepro0212
English.
9783540355953 3540355952 3540355936 9783540355939 1280700300 9781280700309 6610700303 9786610700301
10.1007/3-540-35593-6 doi 10.1007/3-540-35593-
978-3-540-35593-9 Springer http://www.springerlink.com
2006930097
GBA699896 bnb
DE-101 013610189 Uk 980746027 GyFmDB
Symbolic dynamics.
Topological dynamics.
Differentiable dynamical systems.
Dynamique symbolique.
Dynamique topologique.
Dynamique différentiable.
MATHEMATICS--Differential Equations--General.
Dinámica topológica
Sistemas dinámicos diferenciables
Differentiable dynamical systems
Symbolic dynamics
Topological dynamics
Symbolische Dynamik
Dynamische systemen.
Grafen.
Algoritmen.
Dynamisches System--Graphentheorie
Graphentheorie--Dynamisches System
Dynamisches System
Topologie
Differentiable dynamical systems.
Symbolic dynamics.
Topological dynamics.
Conference papers and proceedings
QA614.85 / .O84 2007eb
515.39
Dynamical systems, graphs, and algorithms / George Osipenko. - Berlin ; New York : Springer, ©2007. - 1 online resource (xii, 283 pages) : illustrations - Lecture notes in mathematics, 1889 0075-8434 ; . - Lecture notes in mathematics (Springer-Verlag) ; 1889. .
Includes bibliographical references and index.
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 -- [Appendix] A. Double logistic map -- [Appendix] B. Implementation of the symbolic image.
Use copy
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.
Electronic reproduction.
[Place of publication not identified] :
HathiTrust Digital Library,
2010.
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
http://purl.oclc.org/DLF/benchrepro0212
English.
9783540355953 3540355952 3540355936 9783540355939 1280700300 9781280700309 6610700303 9786610700301
10.1007/3-540-35593-6 doi 10.1007/3-540-35593-
978-3-540-35593-9 Springer http://www.springerlink.com
2006930097
GBA699896 bnb
DE-101 013610189 Uk 980746027 GyFmDB
Symbolic dynamics.
Topological dynamics.
Differentiable dynamical systems.
Dynamique symbolique.
Dynamique topologique.
Dynamique différentiable.
MATHEMATICS--Differential Equations--General.
Dinámica topológica
Sistemas dinámicos diferenciables
Differentiable dynamical systems
Symbolic dynamics
Topological dynamics
Symbolische Dynamik
Dynamische systemen.
Grafen.
Algoritmen.
Dynamisches System--Graphentheorie
Graphentheorie--Dynamisches System
Dynamisches System
Topologie
Differentiable dynamical systems.
Symbolic dynamics.
Topological dynamics.
Conference papers and proceedings
QA614.85 / .O84 2007eb
515.39