Pseudo-orbits, pseudoleaves and geometric entropy of foliations

TL;DR

This paper demonstrates that the entropy of finitely generated pseudogroups and foliations on compact Riemannian manifolds can be computed through counting separated pseudo-orbits and pseudoleaves, respectively.

Contribution

It introduces a method to calculate entropy of pseudogroups and foliations using separated pseudo-orbits and pseudoleaves, linking geometric structures with entropy measurement.

Findings

Entropy can be computed via counting separated pseudo-orbits.

Entropy of foliations can be determined by counting pseudoleaves.

The approach provides a new way to analyze geometric entropy in foliations.

Abstract

We show that the entropy of a finitely generated pseudogroup (resp., of a foliation of a compact Riemannian manifold) can be calculated by suitable counting separated pseudo-orbits (resp., pseudoleaves).