Positive topological entropy implies chaos DC2
Positive topological entropy implies chaos DC2
Using methods of entropy in ergodic theory, we prove that positive topological entropy implies chaos DC2. That is, if a system $(X,T)$ has positive topological entropy, then there exists an uncountable set $E$ such that for any two distinct points $x,y$ in $E$, \[ \liminf _{n\to \infty } \frac 1n …