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