Stabilization of hyperbolic chaos by the Pyragas method

Белякин, С.Т.

Автор: Белякин С.Т.
Сборник: XXXIV Dynamics Days Europe
Серия: 34
Том: 1
Тезисы
Год издания: 2014
Место издания: Dynamics Days Europe
Первая страница: 204
Последняя страница: 204
Аннотация: Hyperbolicity is a fundamental feature of chaotic systems. It is as follows: a tangent space of such systems is a combination of three subspaces; stable, E(s) unstable E(u) and neutral E(0). Close trajectories which correspond to E(s) converge exponentially to each other when t ! +1, and those which correspond to E(u) - when t ! ��1. In the subspace E(0) the vectors contract and expand more slowly than the exponential velocity. When the degree of contraction and expansion in the subspaces E(s) and E(u) changes from point to point along the trajectory, such systems are called non- uniformly hyperbolic. Dynamic systems with uniform hyperbolicity of all the trajectories are called Amosov systems. If the system under consideration is dissipative, i.e. some contraction of the phase volume takes place, then in this case chaos is provided by the availability of the hyperbolic attractor. Each trajectory belonging to such an attractor possesses the property of hyperbolicity. The hyperbolic attractor is structurally stable and possesses SRB - measure ( i.e. the measure of Sinai-Ruelle-Bowen ) and corresponding systems are K-systems, for which the conditions of the central limit theorem are obeyed.
Добавил в систему: Белякин Сергей Тихонович

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