MSC2010 34C23, 34D45

Examples of strange attractors in three-dimentional nonoriented maps

A. D. Kozlov1

Annotation We consider the problem of exsistance of descrete strange attractors, i.e. attrators which posess only one fixed point, in three-dimentional nonoriented diffeomorphisms. In this article we solve this problem using three-dimentional nonoriented generalized H\'enon maps, i.e. polynomial maps with constant Jacobian. We show that such maps can posses nonoriented descrete homoclinic attractors of different types. Herewith the main attention in this work is given to the description of qualitative and numerical methods which is used to find such attractors (the saddle chart, colored Lyapunov diagram) as well as to the description of geometric structures of attractors. Examples of various nonoriented strange attractors found in specific three-dimensional maps using the above methods are also given.
Keywordschaos, strange homoclinic attractors, spiral attractor, three-dimentional H\'enon map, saddle chart, colored Lyapunov diagram

1Alexander D. Kozlov, junior researcher, Supercomputer technology laboratory, IITMM, N.I. Lobachevsky State University of Nizhni Novgorod – National Research University (23 Prospekt Gagarina (Gagarin Avenue) BLDG 2, 2nd floor, 603950 Nizhni Novgorod, Russia); junior researcher, Laboratory of topological methods in dynamics, National Research University Higher School of Economics (25/12 Bolshaja Pecherskaja Str., Nizhni Novgorod 603155, Russia), ORCID:,

Citation: A. D. Kozlov, "[Examples of strange attractors in three-dimentional nonoriented maps]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,19:2 (2017) 62–75 (In Russian)

DOI 10.15507/2079-6900.19.201701.062-075