Propri\'et\'es dynamiques g\'en\'eriques des hom\'eomorphismes conservatifs

TL;DR

This paper investigates the typical dynamic behaviors of conservative homeomorphisms on compact manifolds, highlighting key techniques like periodic approximations and embedding in bi-measurable automorphisms.

Contribution

It introduces new methods for proving generic properties of conservative homeomorphisms, emphasizing the role of periodic approximations and embeddings.

Findings

Periodic approximations are crucial for genericity results.

Embedding homeomorphisms into bi-measurable automorphisms aids analysis.

The paper establishes generic dynamical properties for conservative homeomorphisms.

Abstract

This memoir is concerned with the generic dynamical properties of conservative homeomorphisms of compact manifolds. Several important techniques allowing to prove genericity results are presented: we emphasize the important role played by periodic approximations of homeomorphisms, and by the embedding of the space of homeomorphisms in the space of bi-measurable automorphisms.