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Zhurnal SVMO, 2017, Volume 19, Number 2, Pages 62–75 (Mi svmo660)  

This article is cited in 1 scientific paper (total in 1 paper)

Mathematics

Examples of strange attractors in three-dimentional nonoriented maps

A. D. Kozlovab

a Lobachevski State University of Nizhni Novgorod
b National Research University – Higher School of Economics in Nizhny Novgorod

Abstract: We consider the problem of existance of discrete strangehomoclinic attractors (i.e. attrators which posess exactly one fixed point) for three-dimensional non-oriented diffeomorphisms. In this article we solve this problem using three-dimensional non-oriented generalized Hénon maps, i.e. polynomial maps with constant and negative Jacobian. We show that such maps can posses non-oriented discrete homoclinic attractors of different types. Herewith the main attention in this work is paid to the description of qualitative and numerical methods which are used to find such attractors (the saddle chart, colored Lyapunov diagram) as well as to the description of attractors’ geometric structures. Examples of various non-oriented strange attractors that were found in specific three-dimensional maps by means of above listed methods are also given.

Keywords: chaos, strange homoclinic attractors, spiral attractor, three-dimentional Hénon map, saddle chart, colored Lyapunov diagram

Funding Agency Grant Number
Russian Science Foundation 14-41-00044
17-11-01041


DOI: https://doi.org/10.15507/2079-6900.19.201701.062-075

Full text: PDF file (1104 kB)
References: PDF file   HTML file

UDC: 517.9
MSC: Primary 34C23; Secondary 34D45

Citation: A. D. Kozlov, “Examples of strange attractors in three-dimentional nonoriented maps”, Zhurnal SVMO, 19:2 (2017), 62–75

Citation in format AMSBIB
\Bibitem{Koz17}
\by A.~D.~Kozlov
\paper Examples of strange attractors in three-dimentional nonoriented maps
\jour Zhurnal SVMO
\yr 2017
\vol 19
\issue 2
\pages 62--75
\mathnet{http://mi.mathnet.ru/svmo660}
\crossref{https://doi.org/10.15507/2079-6900.19.201701.062-075}
\elib{https://elibrary.ru/item.asp?id=29783062}


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    This publication is cited in the following articles:
    1. A. O. Kazakov, E. Yu. Karatetskaya, A. D. Kozlov, K. A. Safonov, “O klassifikatsii gomoklinicheskikh attraktorov trekhmernykh potokov”, Zhurnal SVMO, 21:4 (2019), 443–459  mathnet  crossref
  • Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva
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