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Math Help - Circle homeomorphism without periodic point

  1. #1
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    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?
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  2. #2
    Senior Member roninpro's Avatar
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    What is meant by "orbit"? Orbit as in: pick a point x and repeatedly apply f to it?
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  3. #3
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    [LaTeX ERROR: Convert failed] define [Math]Orbit(x) = \{f^{n}(x) | n \in \mathbb_{Z}\}[/tex]
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