On three types of dynamics, and the notion of attractor
File(s)
Accepted version
Author(s)
Turaev, D
Gonchenko, S
Type
Journal Article
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.
Date Issued
2017-09-01
Date Acceptance
2017-06-16
Citation
Proceedings of the Steklov Institute of Mathematics, 2017, 297 (1), pp.116-137
ISSN
0081-5438
Publisher
Springer
Start Page
116
End Page
137
Journal / Book Title
Proceedings of the Steklov Institute of Mathematics
Volume
297
Issue
1
Copyright Statement
© Pleiades Publishing, Ltd. 2017. Gonchenko, S.V. & Turaev, D.V. Proc. Steklov Inst. Math. (2017) 297: 116. https://doi.org/10.1134/S0081543817040071
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Grant Number
EP/P026001/1
Subjects
math.DS
0101 Pure Mathematics
0102 Applied Mathematics
Publication Status
Published