# Exploding Markov operators

## TL;DR

This paper introduces a special class of doubly stochastic Markov operators derived from measure-preserving transformations, which retain properties like ergodicity and positive entropy but may lack pointwise factors.

## Contribution

It constructs a new class of Markov operators that preserve measure and exhibit key ergodic properties without necessarily having pointwise factors.

## Key findings

- Operators inherit ergodicity and positive entropy.
- They may lack pointwise factors.
- New class expands understanding of measure-preserving transformations.

## Abstract

A special class of doubly stochastic (Markov) operators is constructed. These operators come from measure preserving transformations and inherit some of their properties, namely ergodicity and positivity of entropy, yet they may have no pointwise factors.