Homoclinic invariants of ergodic actions

TL;DR

This paper introduces homoclinic invariants for ergodic actions, exploring their relationships with various dynamical properties and demonstrating their realization in Gaussian and Poisson suspension models.

Contribution

It defines new homoclinic invariants for measure-preserving actions and establishes their connections with key ergodic properties, providing realizations in specific suspension systems.

Findings

Homoclinic invariants relate to factors, full groups, and ranks.

Connections established with rigidity and multiple mixing.

Realizations achieved in Gaussian and Poisson suspensions.

Abstract

We consider a family of homoclinic groups and Gordin's type invariants of measure-preserving actions, state their connections with factors, full groups, ranks, rigidity, multiple mixing and realize such invariants in the class of Gaussian and Poisson suspensions.