Density of the set of symbolic dynamics with all ergodic measures supported on periodic orbits
Volume 231 / 2015
Fundamenta Mathematicae 231 (2015), 93-99
MSC: Primary 37B10; Secondary 37A05, 37D35.
DOI: 10.4064/fm231-1-6
Abstract
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 $\omega$-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 $\widetilde T:K\rightarrow K$ with every orbit finally periodic.
