%0 Journal Article
%T Aperiodic homeomorphisms approximate chain mixing endomorphisms on the Cantor set
%A Takashi Shimomura
%J Mathematics
%D 2015
%I arXiv
%X Let $f$ be a chain mixing continuous onto mapping from the Cantor set onto itself.Let $g$ be an aperiodic homeomorphism on the Cantor set. We show that homeomorphisms that are topologically conjugate to g approximate $f$ in the topology of uniform convergence if a trivial necessary condition on periodic points is satisfied.In particular, let $f$ be a chain mixing continuous onto mapping from the Cantor set onto itself with a fixed point and g, an aperiodic homeomorphism on the Cantor set. Then, homeomorphisms that are topologically conjugate to $g$ approximate $f$.
%U http://arxiv.org/abs/1506.07663v1