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This article is cited in 47 scientific papers (total in 47 papers)
On three types of dynamics and the notion of attractor
S. V. Gonchenkoa, D. V. Turaevab a Lobachevsky State University of Nizhni Novgorod, pr. Gagarina 23, Nizhni Novgorod, 603950 Russia
b Department of Mathematics, Imperial College London, London SW7 2AZ, UK
Abstract:
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.
Received: February 27, 2017
Citation:
S. V. Gonchenko, D. V. Turaev, “On three types of dynamics and the notion of attractor”, Order and chaos in dynamical systems, Collected papers. On the occasion of the 125th anniversary of the birth of Academician Dmitry Victorovich Anosov, Trudy Mat. Inst. Steklova, 297, MAIK Nauka/Interperiodica, Moscow, 2017, 133–157; Proc. Steklov Inst. Math., 297 (2017), 116–137
Linking options:
https://www.mathnet.ru/eng/tm3822https://doi.org/10.1134/S0371968517020078 https://www.mathnet.ru/eng/tm/v297/p133
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