$C^1$ weak Palis conjecture for nonsingular flows

TL;DR

This paper proves the $C^1$ weak Palis conjecture for nonsingular flows, showing that generically such flows are either Morse-Smale or have horseshoes, by adapting Crovisier's central model method.

Contribution

It extends Crovisier's central model approach from diffeomorphisms to nonsingular flows to establish the $C^1$ weak Palis conjecture.

Findings

Proves $C^1$ weak Palis conjecture for nonsingular flows.

Shows generic flows are Morse-Smale or exhibit horseshoes.

Adapts methods from diffeomorphisms to flows.

Abstract

The aim of this work is to prove $C^1$ weak Palis conjecture for nonsingular flows. Weak Palis conjecture claims that a generic vector field either is Morse-Smale or exhibits horseshoes. Central model is come up with by Crovisier to obtain homoclinic intersection for diffeomorphisms. We adapt his method for nonsingular flows.