0

Let $(X, d)$ be a compact metric space and $f:X\to X$ be an expansive homeomorphism. This means that there is $c>0$ such that if $x\neq y$, then there is $n\in\mathbb{Z}$, such that $d(f^n(x), f^n(y))>c$.

It is known that if $f$ is expansive, then the set of periodic points is countable and also the set of fixed points of $f$ is finite.

Let $f:X\to X$ is expansive and for $x\in X$, $\omega(x, f)\subseteq Per(f)$. In a paper author claimed that $\omega(x, f)$ is finite. I do not understand it. Please help me.

user479859
  • 1,287
  • An infinite set of periodic points would have an accumulation point. Wouldn't the period be constant in a neighborhood of that point? If so this contradicts expansivity. – John B Dec 15 '17 at 22:58
  • What a beautiful function name! :-) – md2perpe Dec 16 '17 at 09:26

0 Answers0