Symbolic Analysis of Dynamical Systems

George Osipenko (Autor)

Buch | Softcover

226 Seiten

2025
Springer Verlag, Singapore
978-981-95-0712-2 (ISBN)

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This book is devoted to the study of the global properties of the dynamical systems. It gives a justification of using numerical methods for solving several problems such as localization of a chain-recurrent set of trajectories, construction of attractors and their domains of attraction, construction of filtrations, calculation of invariant measures, approximation of ergodic measures, estimation of the entropy of a dynamical system, calculation of the averaging spectrum of a function, calculation of the Morse spectrum, a test for the hyperbolicity of a dynamical system. The book is intended for researchers in dynamical systems and their applications in many scientific and technical disciplines, including engineering, physics, chemistry, biology, economics, and demography.

George Osipenko is Professor in the Department of Applied Mathematics, Moscow State University, branch in Sevastopol, Russia, since 2015. Earlier, he taught at the Institute of Banking in Sevastopol, from 2010–2014. He taught at the Sevastopol Polytechnic Institute, from 2006–2009. He also taught at the St. Petersburg (Leningrad) Polytechnic Institute of Peter the Great, from 1975–2005. He completed his graduation and post-graduation in mathematics from the Faculty of Mathematics and Mechanics of the Leningrad University, Russia, respectively in 1972 and 1975. He defended his doctoral dissertation and received a professor’s degree, in 1990. He is awarded the N.N. Bogolyubova award, in 2009.

Introduction.- Symbolic Image of Dynamic System.- Shadowing of Trajectories.- Attractors and Filtrations.- Invariant measures.- Ergodic Measures.- Entropy.- Averaging.- Lyapunov Exponent.- Numerical Exploration.- Appendix.

Erscheinungsdatum	13.11.2025
Reihe/Serie	Mathematical Marvels: Texts and Monographs in the Spirit of CR Rao
Zusatzinfo	13 Illustrations, color; 25 Illustrations, black and white
Verlagsort	Singapore
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	attractor • Averaging • Chain-recurrent set • complex (chaotic) behavior of solutions • Dynamical Systems • Entropy • Graph Algorithms • homoclinic and heteroclinic solutions • hyperbolicity • hyperbolic orbits and sets • invariant measures • Lyapunov exponent • Measure-Preserving Transformations • shadowing • Structural Stability • symbolic dynamics • Symbolic image • topological structure
ISBN-10	981-95-0712-X / 981950712X
ISBN-13	978-981-95-0712-2 / 9789819507122
Zustand	Neuware