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Izvestiya VUZ. Applied Nonlinear Dynamics, 2024, Volume 32, Issue 6, Pages 722–765
DOI: https://doi.org/10.18500/0869-6632-003138 (Mi ivp618) 		 
BIFURCATION IN DYNAMICAL SYSTEMS. DETERMINISTIC CHAOS. QUANTUM CHAOS

Mixed dynamics: elements of theory and examples

S. V. Gonchenkoab, A. S. Gonchenkoab, A. O. Kazakova, E. A. Samylinaa

a National Research University Higher School of Economics, Nizhny Novgorod, Russia
b National Research Lobachevsky State University of Nizhny Novgorod, Russia
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DOI: https://doi.org/10.18500/0869-6632-003138
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.
Keywords: dynamical chaos, mixed dynamics, CRH-attractor, full attractor, absolute Newhouse domain
Funding agency Grant number
Russian Science Foundation 24-11-00339
23-71-30008
Ministry of Science and Higher Education of the Russian Federation FSWR-2020-0036
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.
Received: 15.07.2024
Accepted: 04.08.2024
Bibliographic databases:
Document Type: Article
UDC: 517.925 + 517.93
Language: Russian
Citation: S. V. Gonchenko, A. S. Gonchenko, A. O. Kazakov, E. A. Samylina, “Mixed dynamics: elements of theory and examples”, Izvestiya VUZ. Applied Nonlinear Dynamics, 32:6 (2024), 722–765
Citation in format AMSBIB
\Bibitem{GonGonKaz24}
\by S.~V.~Gonchenko, A.~S.~Gonchenko, A.~O.~Kazakov, E.~A.~Samylina
\paper Mixed dynamics: elements of theory and examples
\jour Izvestiya VUZ. Applied Nonlinear Dynamics
\yr 2024
\vol 32
\issue 6
\pages 722--765
\mathnet{http://mi.mathnet.ru/ivp618}
\crossref{https://doi.org/10.18500/0869-6632-003138}
\edn{https://elibrary.ru/PFFDTK}
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