A STRANGE ATTRACTOR WITH LARGE ENTROPY IN THE UNFOLDING OF A LOW RESONANT DEGENERATE HOMOCLINIC ORBIT-Reference-Cited by-同舟云学术

A STRANGE ATTRACTOR WITH LARGE ENTROPY IN THE UNFOLDING OF A LOW RESONANT DEGENERATE HOMOCLINIC ORBIT

Published:2006-12 Issue:12 Volume:16 Page:3509-3522
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

MARTENS M.¹,NAUDOT V.²,YANG J.³

Affiliation:

1. Department of Mathematics, University of Groningen, P. O. Box 800, 9700 AV Groningen, The Netherlands

2. Institute of Mathematics, Warwick University, Gibbet Hill Road, CV4 7AL Coventry, UK

3. LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127406016951

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