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arXiv · 1705.04389

On three types of dynamics, and the notion of attractor

Sergey Gonchenko·Dmitry Turaev
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Abstract

We propose a theoretical framework for an explanation of the numerically discovered phenomenon of the attractor-repeller merger. We identify regimes which are observed in dynamical systems with attractors as defined in a work by Ruelle and show that these attractors can be of three different types. The first two types correspond to th ewell-known types of chaotic behavior - conservative and dissipative, while the attractors of the third type, the 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.

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Sergey Gonchenko, Dmitry Turaev. 2017-05-11. On three types of dynamics, and the notion of attractor. https://arxiv.org/abs/1705.04389

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