Invariant measures for discrete dynamical systems and ergodic properties of generalized Boole type transformations

TL;DR

This paper investigates invariant measures and ergodic properties of generalized Boole type transformations, introducing new two-dimensional variants and employing an invariant quasi-measure approach based on the Frobenius--Perron operator.

Contribution

It presents a novel method for analyzing invariant measures using quasi-measures and introduces new two-dimensional transformations with their ergodic properties.

Findings

Identification of invariant measures for generalized Boole transformations

Introduction of new two-dimensional Boole type transformations

Analysis of ergodicity properties of these transformations

Abstract

Invariant ergodic measures for generalized Boole type transformations are studied using an invariant quasi-measure generating function approach based on special solutions to the Frobenius--Perron operator. New two-dimensional Boole type transformations are introduced, and their invariant measures and ergodicity properties are analyzed.