1

Let $f:M\rightarrow M$ be a homeomorphism. $f$ is called a $c$-expansive homeomorphism, whenever for every $x\neq y$, there is an integer $n$ with $d(f^n (x),f^n (y))>c$.

By double asymptotically points, we mean about two points $x$ and $y$ such that $d(f^n (x),f^n (y))$ tends to zero whenever $n$ tends to $\pm \infty$.

Question: Does there exist an example of an expansive homeomorphism $f$ in an infinite compact metric space $M$ without double asymptotically points?

David Kraemer
  • 1,672
Cocón
  • 11

1 Answers1

0

Yes, there is an expansive homeomorphism on compact metric space without double asymptotically points. Consider for example the following link, page: 32

https://www.researchgate.net/publication/284900645_Expansive_Dynamical_Systems

user479859
  • 1,287
  • Thanks. I know this example, but i do not know how to prove the nonexistence of double asymptotically points. – Cocón Oct 17 '19 at 23:31