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Simple Scenarios of Onset of Chaos in Three-Dimensional Maps

Research Institute of Applied Mathematics and Cybernetics, Lobachevsky State University of Nizhny Novgorod, ul. Ulyanova 10, Nizhny Novgorod 603005, Russia

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Sergey Gonchenko

Research Institute of Applied Mathematics and Cybernetics, Lobachevsky State University of Nizhny Novgorod, ul. Ulyanova 10, Nizhny Novgorod 603005, Russia

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Alexey Kazakov

Research Institute of Applied Mathematics and Cybernetics, Lobachevsky State University of Nizhny Novgorod, ul. Ulyanova 10, Nizhny Novgorod 603005, Russia

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, and

Dmitry Turaev

Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom

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https://doi.org/10.1142/S0218127414400057Cited by:42 (Source: Crossref)

Abstract

We give a qualitative description of two main routes to chaos in three-dimensional maps. We discuss Shilnikov scenario of transition to spiral chaos and a scenario of transition to discrete Lorenz-like and figure-eight strange attractors. The theory is illustrated by numerical analysis of three-dimensional Henon-like maps and Poincaré maps in models of nonholonomic mechanics.

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