Recurrent surface homeomorphisms

Recurrent Surface Homeomorphisms

An orientation-preserving recurrent homeomorphism of the twosphere which is not the identity is shown to admit exactly two fixed points. A recurrent homeomorphism of a compact surface with negative Euler characteristic is periodic.

Simple Braids for Surface Homeomorphisms

Let S be a compact, oriented surface with negative Euler characteristic and let f : S → S be a homeomorphism isotopic to the identity. If there exists a periodic orbit with a non-zero rotation vector (~ p, q), then there exists a simple braid with the same rotation vector.

Component Orbits under Pointwise Recurrent Homeomorphisms

Surface Homeomorphisms with Zero Dimensional Singular Set

We prove that if f is an orientation-preserving homeomorphism of a closed orientable surface M whose singular set Σ(f) is totally disconnected, then f is topologically conjugate to a conformal transformation.

On the Classification of Surface Homeomorphisms

The purpose of this article is to give a brief and elementary approach to the classification of mapping-classes for a surface with negative Euler characteristic. Work of Thurston ([9], [10], [7]) has brought out a deep analogy with the classical structure of the modular group SL2(Z) acting on the upper half plane H by constructing a completion of L, the space of simple loops in a base surface v...