Persistent antimonotonic bifurcations and strange attractors for cubic homoclinic tangencies

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dc.creatorKiriki, Shin
dc.creatorSoma, Teruhiko
dc.date2008-03-20
dc.date.accessioned2026-07-07T09:33:38Z
dc.date.available2026-07-07T09:33:38Z
dc.descriptionIn 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.
dc.description39 pages, 22 figures. To appear in Nonlinearity (accepted 20, March 2008)
dc.identifierhttps://arxiv.org/abs/0803.2916
dc.identifierhttp://arxiv.org/abs/0803.2916
dc.identifierNonlinearity 21 (2008) 1105-1140
dc.identifierdoi:10.1088/0951-7715/21/5/011
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159200
dc.subjectDynamical Systems
dc.subject37C29;37D45
dc.titlePersistent antimonotonic bifurcations and strange attractors for cubic homoclinic tangencies
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