ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Gonchenko S. V., Gonchenko A. S., Kazakov A. O., Самылина Е. А. Mixed dynamics: elements of theory and examples. Izvestiya VUZ. Applied Nonlinear Dynamics, 2024, vol. 32, iss. 6, pp. 722-765. DOI: 10.18500/0869-6632-003138, EDN: PFFDTK

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Heading: 
Bifurcation in Dynamical Systems. Deterministic Chaos. Quantum Chaos.
Article type: 
Article
UDC: 
517.925 + 517.93
DOI: 
10.18500/0869-6632-003138
EDN: 
PFFDTK

Mixed dynamics: elements of theory and examples

Autors: 
Gonchenko Sergey Vladimirovich, Lobachevsky State University of Nizhny Novgorod
Gonchenko Aleksandr Sergeevich, Lobachevsky State University of Nizhny Novgorod
Kazakov Alexey Olegovich, National Research University "Higher School of Economics"
Самылина Евгения Александровна, National Research University "Higher School of Economics"
Abstract: 

The main goal of the paper is to present recent results obtained in the mathematical theory of dynamical chaos and related to the discovery of its new, third, form, the so-called mixed dynamics. This type of chaos is very different from its two classical forms, conservative and dissipative chaos, and its main difference is that attractors and repellers can intersect without coinciding.

The main results of the paper are related to construction of theoretical schemes aimed to mathematical justification of this phenomenon using the most general methods of topological dynamics. The paper also provides a number of examples of systems from applications in which mixed dynamics is observed. It is shown that such dynamics can be of different types, from close to conservative to strongly dissipative, and also that it can arise as a result of various bifurcation mechanisms.

Key words: 
dynamical chaos
mixed dynamics
CRH-attractor
full attractor
absolute Newhouse domain
Acknowledgments: 
The work was supported by the Russian Science Foundation grant No. 24-11-00339 (section 1), the Russian Science Foundation grant No. 23-71-30008 (section 2). Research in section 3.1 was carried out within the framework of the grant FSWR-2020-0036 of the Ministry of Science and Higher Education of the Russian Federation. The studies in sections 3.2 and 3.3 were carried out with the financial support of the fundamental research program of the National Research University Higher School of Economics.
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Received: 
15.07.2024
Accepted: 
04.08.2024
Available online: 
26.11.2024
Published: 
29.11.2024
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