Stability under C^1-perturbation of dynamical system

Авторы: Osipenko G.S., Korzh T.N.
Журнал: Research and Reports on Mathematics
Том: 1
Номер: 1
Год издания: 2017
Первая страница: 1
Последняя страница: 9
Аннотация: The aim is substantiation of a constructive method for verification of structural stability of discrete dynamical systems. The hyperbolicity of the chain recurrent set is a necessary condition for the structural stability. If the spectrum of the differential Df does not contain 0, then the chain recurrent set is hyperbolic and the system is Ω-stable. The spectrum is estimated through the symbolic image of operation of the differential on projective bundle. A diffeomorphism f is shown to be structurally stable if and only if the spectrum of complementary differential D ̂f does not contain 0 and there is no connection 〖CR〗^+→〖CR〗^- on the projective bundle, where 〖CR〗^+ and 〖CR〗^- denote the chain recurrent components for the positive and negative parts of the spectrum. These conditions are verified through the symbolic image of the complementary differential.
Добавил в систему: Осипенко Георгий Сергеевич

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