Transitivity of generic semigroups of area-preserving surface diffeomorphisms

TL;DR

This paper proves that for a generic pair of area-preserving surface diffeomorphisms, the semigroup they generate acts transitively on the surface, indicating rich dynamical behavior.

Contribution

It establishes the transitivity of the semigroup generated by generic pairs of area-preserving surface diffeomorphisms, a new result in dynamical systems theory.

Findings

Semigroup action is transitive for generic pairs.

Results apply to compact orientable surfaces.

Advances understanding of surface diffeomorphism dynamics.

Abstract

We prove that the action of the semigroup generated by a $C^r$ generic pair of area-preserving diffeomorphisms of a compact orientable surface is transitive.