Historic and physical wandering domains for wild blender-horseshoes

Abstract

Abstract We present diffeomorphisms of wild blender-horseshoes which belong to C r   ( 1 ⩽ r < ∞ ) closures of two types of diffeomorphisms, one of which has a historic contracting wandering domain, and the other has a non-trivial Dirac physical measure supported by saddle periodic orbit. It is a non-trivial extension of Colli–Vargas’ model (Colli and Vargas 2001 Ergod. Theory Dyn. Syst. 21 1657–81) to the higher dimensional dynamics with the use of wild blender-horseshoes.