Skip to main content
2 of 3
added 197 characters in body
R W
  • 17k
  • 3
  • 37
  • 74

Not at all. Take $f(x)=x^2$ on the unit interval. For examples of uniquely ergodic homeomorphisms of the Cantor set see The prevalence of uniquely ergodic systems by Jewett.

R W
  • 17k
  • 3
  • 37
  • 74