A method of defining central and Gibbs measures and the ergodic method

TL;DR

This paper introduces a general approach to defining invariant measures with specific properties using an ergodic perturbation method, contributing to the understanding of measure construction in dynamical systems.

Contribution

It proposes a novel ergodic perturbation technique for characterizing invariant measures with desired properties.

Findings

Provides a general framework for defining invariant measures.

Introduces an ergodic perturbation method for measure description.

Enhances understanding of measure invariance in dynamical systems.

Abstract

We formulate a general statement of the problem of defining invariant measures with certain properties and suggest an ergodic method of perturbations for describing such measures.