Topological stability for conservative systems

TL;DR

This paper establishes that topologically stable incompressible flows in the C1 topology are essentially Anosov flows, extending the result to both continuous and discrete-time systems.

Contribution

It proves that the C1-interior of topologically stable incompressible flows consists only of Anosov flows, providing a significant stability characterization.

Findings

C1-interior of topologically stable flows is contained in Anosov flows

Results extend to discrete-time systems

Provides a stability classification for incompressible flows

Abstract

We prove that the C1-interior of the set of all topologically stable C1-incompressible flows is contained in the set of Anosov incompressible flows. Moreover, we obtain an analogous result for the discrete-time case.