$C^1$-robust strong pluripotency for blender-horseshoes

Abstract: Suppose that $M$ is a closed manifold of dimension greater than two. We show that there exists a $C<sup>1$-diffeomorphism $f_0:M\longrightarrow M$ with a wild affine blender-horseshoe $Λ<em>{f_0}$ such that any element $f$ of $\mathrm{Diff}<sup>1(M)$ sufficiently $C<sup>1$-close to $f_0$ is strongly pluripotent for the continuation $Λ_f<sup>{(\mathrm{mj})}$ of $Λ</em>{f_0}<sup>{(\mathrm{mj})}$, where $Λ<em>{f_0}<sup>{(\mathrm{mj})}$ is the dense subset of $Λ</em>{f_0}$ consisting of elements with majority condition.