On global bifurcations in three-dimensional diffeomorphisms leading to wild Lorenz-like attractors

S. V. Gonchenko; L. P. Shilnikov; D. V. Turaev

doi:10.1134/S1560354709010092

On global bifurcations in three-dimensional diffeomorphisms leading to wild Lorenz-like attractors

S. V. Gonchenko, L. P. Shilnikov, D. V. Turaev

Department of Mathematics

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

38 Scopus citations

Abstract

We study dynamics and bifurcations of three-dimensional diffeomorphisms with nontransverse heteroclinic cycles. We show that bifurcations under consideration lead to the birth of wild-hyperbolic Lorenz attractors. These attractors can be viewed as periodically perturbed classical Lorenz attractors, however, they allow for the existence of homoclinic tangencies and, hence, wild hyperbolic sets.

Original language	English
Pages (from-to)	137-147
Number of pages	11
Journal	Regular and Chaotic Dynamics
Volume	14
Issue number	1
DOIs	https://doi.org/10.1134/S1560354709010092
State	Published - 1 Jan 2009

Keywords

Homoclinic tangency
Lorenz attractor
Strange attractor
Wild-hyperbolic attractor

ASJC Scopus subject areas

Mathematics (miscellaneous)

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10.1134/S1560354709010092

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abstract = "We study dynamics and bifurcations of three-dimensional diffeomorphisms with nontransverse heteroclinic cycles. We show that bifurcations under consideration lead to the birth of wild-hyperbolic Lorenz attractors. These attractors can be viewed as periodically perturbed classical Lorenz attractors, however, they allow for the existence of homoclinic tangencies and, hence, wild hyperbolic sets.",

keywords = "Homoclinic tangency, Lorenz attractor, Strange attractor, Wild-hyperbolic attractor",

author = "Gonchenko, {S. V.} and Shilnikov, {L. P.} and Turaev, {D. V.}",

note = "Funding Information: We acknowledge support by grants ISF 273/07, MNTI-RFBR No. 06-01-72023, RFBR No.07-01-00566, No.07-01-00715 and No.08-01-00083, and thank Center for Advanced Mathematical Studies (Ben Gurion University) for the hospitality.",

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AU - Gonchenko, S. V.

AU - Shilnikov, L. P.

AU - Turaev, D. V.

N1 - Funding Information: We acknowledge support by grants ISF 273/07, MNTI-RFBR No. 06-01-72023, RFBR No.07-01-00566, No.07-01-00715 and No.08-01-00083, and thank Center for Advanced Mathematical Studies (Ben Gurion University) for the hospitality.

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N2 - We study dynamics and bifurcations of three-dimensional diffeomorphisms with nontransverse heteroclinic cycles. We show that bifurcations under consideration lead to the birth of wild-hyperbolic Lorenz attractors. These attractors can be viewed as periodically perturbed classical Lorenz attractors, however, they allow for the existence of homoclinic tangencies and, hence, wild hyperbolic sets.

AB - We study dynamics and bifurcations of three-dimensional diffeomorphisms with nontransverse heteroclinic cycles. We show that bifurcations under consideration lead to the birth of wild-hyperbolic Lorenz attractors. These attractors can be viewed as periodically perturbed classical Lorenz attractors, however, they allow for the existence of homoclinic tangencies and, hence, wild hyperbolic sets.

KW - Homoclinic tangency

KW - Lorenz attractor

KW - Strange attractor

KW - Wild-hyperbolic attractor

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On global bifurcations in three-dimensional diffeomorphisms leading to wild Lorenz-like attractors

Abstract

Keywords

ASJC Scopus subject areas

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