Ergodic theorem for the differential equations with interaction

TL;DR

This paper investigates the ergodic properties of differential equations with interaction and applies these results to analyze the limiting behavior of braid invariants related to solution flows.

Contribution

It introduces new ergodic theorems for differential equations with interaction and connects these to the study of braid invariants in dynamical systems.

Findings

Established ergodic properties for a class of differential equations with interaction.

Linked ergodic behavior to the limiting behavior of braid invariants.

Provided a framework for analyzing the long-term behavior of solution flows.

Abstract

For a differential equation with interaction, we investigate its ergodic properties. We apply the obtained results to study the limiting behavior of braid invariants associated with the flow of solutions.