Relative tail entropy for random bundle transformations

TL;DR

This paper introduces the concept of relative tail entropy for continuous bundle random dynamical systems, establishing a variational principle and demonstrating its invariance under principal extensions.

Contribution

It presents the novel concept of relative tail entropy and proves its key properties within the context of random dynamical systems.

Findings

Established a variational principle for relative tail entropy.

Proved invariance of relative tail entropy under principal extensions.

Introduced a new entropy measure for random bundle transformations.

Abstract

We introduce the relative tail entropy to establish a variational principle for continuous bundle random dynamical systems. We also show that the relative tail entropy is conserved by the principal extension.