Entropy for actions of free groups under bounded orbit-equivalence

TL;DR

This paper demonstrates that the $f$-invariant, a form of entropy for free group actions, remains unchanged under bounded orbit-equivalence, highlighting its robustness as an invariant.

Contribution

It proves the invariance of the $f$-invariant under bounded orbit-equivalence for free group actions, a significant theoretical advancement.

Findings

$f$-invariant is invariant under bounded orbit-equivalence

Establishes robustness of entropy notion for free group actions

Advances understanding of entropy invariants in dynamical systems

Abstract

The $f$-invariant is a notion of entropy for probability-measure-preserving actions of free groups. We show it is invariant under bounded orbit-equivalence.