# Ergodic measures with infinite entropy

## TL;DR

This paper constructs ergodic measures with infinite entropy for typical maps and homeomorphisms on compact manifolds, and shows sequences of such measures can converge to zero-entropy measures.

## Contribution

It introduces a method to construct ergodic measures with infinite entropy and demonstrates their convergence to zero-entropy measures on compact manifolds.

## Key findings

- Existence of ergodic measures with infinite entropy for typical maps.
- Construction of sequences converging to zero-entropy measures.
- New insights into the entropy spectrum of ergodic measures.

## Abstract

We construct ergodic probability measures with infinite metric entropy for typical continuous maps and homeomorphisms on compact manifolds. We also construct sequences of such measures that converge to a zero-entropy measure.