Doubling of invariant curves and chaos in three-dimensional diffeomorphisms

A. S. Gonchenko; S. V. Gonchenko; D. Turaev

doi:10.1063/5.0068692

Doubling of invariant curves and chaos in three-dimensional diffeomorphisms

A. S. Gonchenko, S. V. Gonchenko, D. Turaev

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

This paper gives a review of doubling bifurcations of closed invariant curves. We also discuss the role of the curve-doubling bifurcations in the formation of chaotic dynamics. In particular, we study scenarios of the emergence of discrete Lorenz and Shilnikov attractors in three-dimensional Hénon maps.

Original language	English
Article number	113130
Journal	Chaos
Volume	31
Issue number	11
DOIs	https://doi.org/10.1063/5.0068692
State	Published - 1 Nov 2021
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy
Applied Mathematics

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10.1063/5.0068692

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title = "Doubling of invariant curves and chaos in three-dimensional diffeomorphisms",

abstract = "This paper gives a review of doubling bifurcations of closed invariant curves. We also discuss the role of the curve-doubling bifurcations in the formation of chaotic dynamics. In particular, we study scenarios of the emergence of discrete Lorenz and Shilnikov attractors in three-dimensional H{\'e}non maps.",

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AU - Turaev, D.

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AB - This paper gives a review of doubling bifurcations of closed invariant curves. We also discuss the role of the curve-doubling bifurcations in the formation of chaotic dynamics. In particular, we study scenarios of the emergence of discrete Lorenz and Shilnikov attractors in three-dimensional Hénon maps.

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Doubling of invariant curves and chaos in three-dimensional diffeomorphisms

Abstract

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