Entropy of foliations with leafwise Finsler structure

TL;DR

This paper extends the concept of geometric entropy to foliations with leafwise Finsler structures, exploring its relation to topological entropy and providing estimates for one-dimensional foliations with Randers structures.

Contribution

It introduces a new framework for geometric entropy in leafwise Finsler foliations and relates it to holonomy and flow entropy, including specific estimates for Randers structures.

Findings

Relation between geometric and topological entropy established

Estimates for one-dimensional foliations with Randers structures provided

Extension of entropy concepts to leafwise Finsler geometry

Abstract

We extend the notion of the geometric entropy of foliation to foliated manifolds equipped with leafwise Finsler structure. We study the relation between the geometric entropy and the topological entropy of the holonomy pseudogroup. The case of foliated manifold with leafwise Randers structure. In this case the estimates for one dimensional foliation defined by a vector field in term of topological entropy of a flow are presented.