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arXiv · 2608.18761

Maximal attractors for perturbations of unimodal maps near a homoclinic tangency

Przemysław Kucharski
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Abstract

We show that small planar perturbations of families of unimodal maps have maximal (equal to the intersection of the iterates of their trapping region) attractors at parameters near homoclinic tangency of one of the fixed points. The results hold for general unimodal maps exhibiting certain hyperbolic properties. Hence, admissible families considered include H\'enon-like families, Lozi-like families, or perturbations of border collision normal forms. Therefore, our results generalize results of Viana in the case of H\'enon-like families and Glendinning and Simpson in the case of border collision normal forms.

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Przemysław Kucharski. 2026-08-19. Maximal attractors for perturbations of unimodal maps near a homoclinic tangency. https://arxiv.org/abs/2608.18761

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