Homeomorphism points and periodic

Question

I don't know how I cen prove that homeomorphism $\mathbb{R}$ can not be periodic points basic period greater than 2.

Could somebody write me solution?

Answer 1

Hints:

1. What are the two main classes of homeomorphisms on ℝ?
2. Only one of these classes can produce a periodic dynamics, which one?
3. Try to draw a period-4 orbit in a cobweb plot with this class of homeomorphism.
4. You will see a simple geometric reason why you fail. Formalise and generalise.