%0 Journal Article
%T Density of the set of symbolic dynamics with all ergodic measures supported on periodic orbits
%A T. C. Batista
%A J. S. Gonschorowski
%A F. A. Tal
%J Mathematics
%D 2014
%I arXiv
%X Let $K$ be the Cantor set. We prove that arbitrarily close to a homeomorphism $T:K\rightarrow K$ there exists a homeomorphism $\widetilde T:K\rightarrow K$ such that the $\alpha$-limit and the $\omega$-limit of every orbit is a periodic orbit. We also prove that arbitrarily close to an endomorphism $T:K\rightarrow K$ there exists an endomorphism $\widetilde T:K\rightarrow K$ close to $T$ such that every orbit is finally periodic.
%U http://arxiv.org/abs/1410.5857v2