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arXiv · 0803.2916

Persistent antimonotonic bifurcations and strange attractors for cubic homoclinic tangencies

Shin Kiriki·Teruhiko Soma
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Abstract

In this paper, we study a two-parameter family of two-dimensional diffeomorphisms such that it has a cubic homoclinic tangency unfolding generically which is associated with a dissipative saddle point. Our first theorem presents an open set in the parameter-plane such that, for any parameter value in the open set, there exists a one-parameter subfamily through this value exhibiting cubically related persistent contact-making and contact-breaking quadratic tangencies. Moreover, the second theorem shows that any such two-parameter family satisfies Wang-Young's conditions which guarantee that it exhibits a cubic polynomial-like strange attractor with an SRB measure.

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Shin Kiriki, Teruhiko Soma. 2008-03-20. Persistent antimonotonic bifurcations and strange attractors for cubic homoclinic tangencies. https://doi.org/10.1088/0951-7715%2F21%2F5%2F011

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