Let be an orientation preserving homeomorphism without a periodic point.
a) Show that if f has a dense orbit, then every orbit is dense.
b) Give a counterexample to the statement that f always has a dense orbit.
Hmm, who can help?
Let be an orientation preserving homeomorphism without a periodic point.
a) Show that if f has a dense orbit, then every orbit is dense.
b) Give a counterexample to the statement that f always has a dense orbit.
Hmm, who can help?