# Weakly homoclinic groups of ergodic actions

## TL;DR

This paper investigates the properties of weakly homoclinic groups in ergodic actions, revealing their structure, connections to factors, and behavior in specific actions like Gauss and Poisson, with implications for ergodic theory.

## Contribution

It provides new insights into the structure and properties of weakly homoclinic groups in various ergodic actions, including their ergodicity and triviality in certain classes.

## Key findings

- Homoclinic groups are full in certain trajectories.
- Weakly homoclinic groups are ergodic for Gauss and Poisson actions.
- Weakly homoclinic groups are trivial for rank-1 actions.

## Abstract

This work contains the following results: the trajectory fullness of the homoclinic groups, their connections with factors, K-property, weak multiple mixing; the ergodicity of the weakly homoclinic group for Gauss and Poisson actions; the triviality of the weakly homoclinic group for classes of rank-1 actions. Some open problems are discussed.