Density of the set of symbolic dynamics with all ergodic measures supported on periodic orbits

作者：Batista Tatiane Cardoso^*; Gonschorowski Juliano dos Santos; Tal Fabio Armando

来源：Fundamenta Mathematicae, 2015, 231(1): 93-99.

DOI：10.4064/fm231-1-6

• ergodic measures
• Cantor set
• periodic orbits

Let K be the Cantor set. We prove that arbitrarily close to a homeomorphism T : K -> K there exists a homeomorphism (T) over tilde : K -> K such that the omega-limit of every orbit is a periodic orbit. We also prove that arbitrarily close to an endomorphism T: K -> K there exists an endomorphism (T) over tilde: K -> K with every orbit finally periodic.

• 出版日期2015