The conjugation method in symplectic dynamics

TL;DR

This paper extends the conjugation method to symplectic and contact dynamics, proving the existence of minimal and strictly ergodic transformations on certain manifolds with circle actions.

Contribution

It adapts the conjugation method to the symplectic and contact setting, establishing new existence results for minimal and ergodic systems.

Findings

Existence of minimal symplectomorphisms on manifolds with circle actions.

Existence of strictly ergodic contactomorphisms on such manifolds.

Method adaptation from Anosov and Katok's conjugation technique.

Abstract

We prove the existence of minimal symplectomorphisms and strictly ergodic contactomorphisms on manifolds which admit a locally free $\mathbb{S}^1$--action by symplectomorphisms and contactomorphisms, respectively. The proof adapts the conjugation method, introduced by Anosov and Katok, to the contact and symplectic setting.