Some advances on generic properties of the Oseledets splitting

TL;DR

This paper surveys recent progress on the generic properties of the Oseledets splitting, focusing on improvements under C1-generic conditions as initially suggested by Mañé, and discusses the current state of research in this area.

Contribution

It provides a comprehensive overview of recent advances and current understanding of the generic properties of the Oseledets splitting under C1 conditions.

Findings

Summarizes key theorems and results in the area

Highlights recent progress and open questions

Provides a survey of the state of the art

Abstract

In his foundational paper [ICM 1983, Warzaw], Ma\~n\'e suggested that some aspects of the Oseledets splitting could be improved if one worked under C1-generic conditions. He announced some powerful theorems, and suggested some lines to follow. Here we survey the state of the art and some recent advances in these directions.