George Osipenko – författare

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.

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.