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

15 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.",

author = "Gonchenko, \{A. S.\} and Gonchenko, \{S. V.\} and D. Turaev",

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AU - Gonchenko, A. S.

AU - Gonchenko, S. V.

AU - Turaev, D.

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Y1 - 2021/11/1

N2 - 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.

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.

UR - https://www.scopus.com/pages/publications/85119590664

U2 - 10.1063/5.0068692

DO - 10.1063/5.0068692

M3 - Article

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AN - SCOPUS:85119590664

SN - 1054-1500

VL - 31

JO - Chaos

JF - Chaos

IS - 11

M1 - 113130

ER -

Doubling of invariant curves and chaos in three-dimensional diffeomorphisms

Abstract

ASJC Scopus subject areas

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