A Difference Set Of A Cantor Set

Abstract. An example of a regular Cantor set whose self-difference set is a Cantor set with a positive measure is given. This is a counter example of one of the questions related to the homoclinic bifurcation of surface diffeomorphisms. \S.0 Introduction. In [2], Palis-Takens investigated the homoclinic bifurcations of surface diffeomorphisms in the following context. Let $M $ be a closed 2-dimensional manifold. We say a $C’-$ diffeomorphism $\phi $ : $Marrow M $ is persistently hyperbolic if there is a $C^{\tau} $-neighborhood $\mathcal{U}$ of $\phi $ and for every $\psi\in \mathcal{U} $ , the non-wandering set $\Omega(\psi) $ is a hyperbolic set (refer [1] for th