On three types of dynamics and the notion of attractor


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We propose a theoretical framework for explaining the numerically discovered phenomenon of the attractor–repeller merger. We identify regimes observed in dynamical systems with attractors as defined in a paper by Ruelle and show that these attractors can be of three different types. The first two types correspond to the well-known types of chaotic behavior, conservative and dissipative, while the attractors of the third type, reversible cores, provide a new type of chaos, the so-called mixed dynamics, characterized by the inseparability of dissipative and conservative regimes. We prove that every elliptic orbit of a generic non-conservative time-reversible system is a reversible core. We also prove that a generic reversible system with an elliptic orbit is universal; i.e., it displays dynamics of maximum possible richness and complexity.

Sobre autores

S. Gonchenko

Lobachevsky State University of Nizhni Novgorod

Autor responsável pela correspondência
Email: sergey.gonchenko@mail.ru
Rússia, pr. Gagarina 23, Nizhny Novgorod, 603950

D. Turaev

Lobachevsky State University of Nizhni Novgorod; Department of Mathematics

Email: sergey.gonchenko@mail.ru
Rússia, pr. Gagarina 23, Nizhny Novgorod, 603950; London, SW7 2AZ

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