A strange attractor with large entropy in the unfolding of a low resonant degenerate homoclinic orbit

M. Martens; V. Naudot; J. Yang

doi:10.1142/S0218127406016951

A strange attractor with large entropy in the unfolding of a low resonant degenerate homoclinic orbit

M. Martens
, V. Naudot
, J. Yang

Mathematics

Stony Brook University

University of Warwick
Peking University

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

6 Scopus citations

Abstract

The unfolding of a vector field exhibiting a degenerate homoclinic orbit of inclination-flip type is studied. The linear part of the unperturbed system possesses a resonance but the coefficient of the corresponding monomial vanishes. We show that for an open set in the parameter space, the system possesses a suspended cubic Hénon-like map. As a consequence, strange attractors with entropy close to log 3 persist in a positive Lebesgue measure set.

Original language	English
Pages (from-to)	3509-3522
Number of pages	14
Journal	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume	16
Issue number	12
DOIs	https://doi.org/10.1142/S0218127406016951
State	Published - Dec 2006

Keywords

Dulac map
Entropy
Hénon-like maps
Strange attractor

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title = "A strange attractor with large entropy in the unfolding of a low resonant degenerate homoclinic orbit",

abstract = "The unfolding of a vector field exhibiting a degenerate homoclinic orbit of inclination-flip type is studied. The linear part of the unperturbed system possesses a resonance but the coefficient of the corresponding monomial vanishes. We show that for an open set in the parameter space, the system possesses a suspended cubic H{\'e}non-like map. As a consequence, strange attractors with entropy close to log 3 persist in a positive Lebesgue measure set.",

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author = "M. Martens and V. Naudot and J. Yang",

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T1 - A strange attractor with large entropy in the unfolding of a low resonant degenerate homoclinic orbit

AU - Martens, M.

AU - Naudot, V.

AU - Yang, J.

PY - 2006/12

Y1 - 2006/12

N2 - The unfolding of a vector field exhibiting a degenerate homoclinic orbit of inclination-flip type is studied. The linear part of the unperturbed system possesses a resonance but the coefficient of the corresponding monomial vanishes. We show that for an open set in the parameter space, the system possesses a suspended cubic Hénon-like map. As a consequence, strange attractors with entropy close to log 3 persist in a positive Lebesgue measure set.

AB - The unfolding of a vector field exhibiting a degenerate homoclinic orbit of inclination-flip type is studied. The linear part of the unperturbed system possesses a resonance but the coefficient of the corresponding monomial vanishes. We show that for an open set in the parameter space, the system possesses a suspended cubic Hénon-like map. As a consequence, strange attractors with entropy close to log 3 persist in a positive Lebesgue measure set.

KW - Dulac map

KW - Entropy

KW - Hénon-like maps

KW - Strange attractor

UR - https://www.scopus.com/pages/publications/33847289739

U2 - 10.1142/S0218127406016951

DO - 10.1142/S0218127406016951

M3 - Article

SN - 0218-1274

VL - 16

SP - 3509

EP - 3522

JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

IS - 12

ER -

A strange attractor with large entropy in the unfolding of a low resonant degenerate homoclinic orbit

Abstract

Keywords

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