Semigroups of locally injective maps and transfer operators

TL;DR

This paper investigates the conditions under which semigroups of continuous, surjective, locally injective maps on compact metric spaces admit transfer operators, contributing to the understanding of their dynamical and operator-theoretic properties.

Contribution

It introduces criteria for the existence of transfer operators for semigroups of locally injective maps, expanding the theoretical framework in dynamical systems.

Findings

Established conditions for transfer operator existence

Characterized semigroups with transfer operators

Linked local injectivity to operator properties

Abstract

We consider semigroups of continuous, surjective, locally injective maps of a compact metric space, and whether such semigroups admit a transfer operator.