Analytic pseudo-rotations displaying ergodicity or emergence on the sphere and disk

TL;DR

This paper constructs analytic pseudo-rotations on the sphere and disk with specific dynamical properties, including ergodicity and maximal local emergence, using advanced approximation techniques.

Contribution

It introduces new analytic pseudo-rotations with controlled ergodic and emergence properties via the Anosov-Katok conjugacy method.

Findings

Constructed ergodic analytic pseudo-rotations on the sphere and disk.

Created pseudo-rotations exhibiting maximum local emergence.

Demonstrated the application of Berger's principle in this context.

Abstract

We construct analytic pseudo-rotations on the sphere and the disk with specific properties. We obtain analytic pseudo-rotations which are ergodic. Then, in opposition to ergodicity, we construct analytic pseudo-rotations which exhibit a maximum order of local emergence. To achieve this, we apply a principle introduced by Berger, based on the Approximation by Conjugacy method of Anosov-Katok.