$C^1$-generic dynamics: tame and wild behaviour

TL;DR

This paper surveys recent findings on the behavior of maximal transitive sets in $C^1$-generic diffeomorphisms, highlighting the distinction between tame and wild dynamics.

Contribution

It provides a comprehensive overview of the recent developments in understanding the structure of transitive sets for $C^1$-generic diffeomorphisms.

Findings

Differentiates between tame and wild behaviors in $C^1$-generic dynamics

Summarizes key results on maximal transitive sets

Highlights open problems and future directions

Abstract

This paper gives a survey of recent results on the maximal transitive sets of $C^1$-generic diffeomorphisms.