Math Help - Circle homeomorphism without periodic point

1. Circle homeomorphism without periodic point

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?

2. What is meant by "orbit"? Orbit as in: pick a point $x$ and repeatedly apply $f$ to it?

3. [LaTeX ERROR: Convert failed] define [Math]Orbit(x) = \{f^{n}(x) | n \in \mathbb_{Z}\}[/tex]