Hénon-Like Families and Blender-Horseshoes at Nontransverse Heterodimensional Cycles

Abstract

In dimension three and under certain regularity assumptions, we construct a renormalization scheme at the heterodimensional tangency of a nontransverse heterodimensional cycle associated with a pair of saddle-foci whose limit dynamics is a center-unstable Hénon-like family displaying blender-horseshoes. As a consequence, the initial cycle can be approximated in higher regularity topologies by diffeomorphisms having blender-horseshoes.