Persistent antimonotonic bifurcations and strange attractors for cubic homoclinic tangencies

Details Persistent antimonotonic bifurcations and strange attractors for cubic homoclinic tangencies Persistent antimonotonic bifurcations and strange attractors for cubic homoclinic tangencies

2008-03-20

arxiv.org/abs/0803.2916v1

Nonlinearity 21 (2008) 1105-1140

Mathematics

Dynamical Systems

39 pages, 22 figures. To appear in Nonlinearity (accepted 20, March 2008)

Scientific paper

10.1088/0951-7715/21/5/011

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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