Blender-horseshoes in center-unstable Hénon-like families

2018/04/07 by Lorenzo J. Díaz, Díaz, Lorenzo J., Sebastián A. Pérez +1
Mathematics · #37C05 #37D05 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:37C05 #msc:37D05

paper · pdf · doi:10.48550/arxiv.1804.02577

22 pages, 8 figures

arxiv created 2018/04/07 · arxiv updated 2018/04/10

Abstract

A blender-horseshoe is a locally maximal transitive hyperbolic set that appears in dimension at least three carrying a distinctive geometrical property: its local stable manifold "behaves" as a manifold of topological dimension greater than the expected one (the dimension of the stable bundle). This property persists under perturbations turning this kind of dynamics an important piece in the global description of robust non-hyperbolic systems. In this paper, we consider a parameterized family of center-unstable Hénon-like of endomorphisms in dimension three and show how blender-horseshoes naturally occur in a specific parameter range.

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