Historic and physical wandering domains for wild blender-horseshoes

We present diffeomorphisms of wild blender-horseshoes which belong to $C^r$ $(1\le r<\mathrm{\infty })$ 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 [CV01] to the higher dimensional dynamics with the use of wild blender-horseshoes.