Measure-preserving semiflows and one-parameter Koopman semigroups

TL;DR

This paper characterizes Markov lattice semigroups generated by measurable semiflows on probability spaces and constructs topological models on compact spaces for these semigroups.

Contribution

It provides a characterization of Markov lattice semigroups via their generators and develops topological models for these semigroups.

Findings

Characterization of Markov lattice semigroups by generator properties

Construction of topological models on compact spaces

Insight into measure-preserving semiflows and Koopman semigroups

Abstract

We characterize Markov lattice semigroups induced by measurable semiflows on probability spaces by properties of their generators. In addition we construct topological models on compact spaces for such semigroups.