Aperiodic homeomorphisms approximate chain mixing endomorphisms on the Cantor set

Abstract

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.