On the ergodic theory of impulsive semiflows

TL;DR

This paper investigates impulsive semiflows, providing conditions for the existence of invariant measures and establishing a Variational Principle, thereby advancing the understanding of their ergodic properties.

Contribution

It introduces specific geometric conditions ensuring invariant measures and proves a Variational Principle for impulsive semiflows.

Findings

Invariant measures exist under certain geometric conditions.

A Variational Principle holds for impulsive semiflows.

Conditions involve the impulsive set and its image being transversal submanifolds.

Abstract

We consider impulsive semiflows and establish sufficient conditions to the existence of invariant measures. Namely, the impulsive set and its image are both submanifolds of codimension one that are transversal to the flow direction. Moreover, we show that under the same conditions a Variational Principle holds.