Pointwise recurrent homeomorphisms with stable fixed points

摘要

We prove that a pointwise recurrent, orientation preserving homeomorphism of the 2-sphere, which is different from the identity and whose fixed points are stable in the sense of Lyapunov must have exactly two fixed points. If moreover there are no periodic points, other than fixed, then every stable minimal set is connected and its complement has exactly two connected components. Finally, we study liftings of the restriction to the complement of the fixed point set to the universal covering space.