Symbolic blender-horseshoes and applications

Abstract

We study partially-hyperbolic skew-product maps over the Bernoulli shift with Hölder dependence on the base points. In the case of contracting fiber maps, symbolic blender-horseshoe is defined as an invariant set which meets any almost horizontal disk in a robust sense. These invariant sets are understood as blenders with center stable bundle of any dimension. We then give necessary conditions (covering property) on an iterated function system such that the relevant skew-product has a symbolic blender-horseshoe. We use this local plug to yield robustly non-hyperbolic transitive diffeomorphisms and robust heterodimensional cycles of co-index equal to the dimension of the central direction.

References in corpus (1)

• A Criterion For Ergodicity of Non-uniformly hyperbolic Diffeomorphisms

Cited by in corpus (10)

• Historic behavior in non-hyperbolic homoclinic classes
• Robust tangencies of large codimension
• Dynamics of iterated function systems on the circle close to rotations
• Persistence of Heterodimensional Cycles
• Expanding actions: minimality and ergodicity
• Robust degenerate unfoldings of cycles and tangencies
• Robust cycles and tangencies of large codimension
• Blender-producing mechanisms and a dichotomy for local dynamics for heterodimensional cycles
• A robustly transitive diffeomorphism of Kan's type
• Equilibrium states for a class of skew-products