On the support of Pollicott-Ruelle resonant states for Anosov flows

TL;DR

This paper proves that all generalized Pollicott-Ruelle resonant states for topologically transitive $C^ $-Anosov flows with any smooth potential are supported everywhere, revealing a fundamental property of these states.

Contribution

It establishes the full support property of resonant states for a broad class of Anosov flows with arbitrary smooth potentials, extending previous results.

Findings

Resonant states have full support for topologically transitive $C^ $-Anosov flows.

Supports the understanding of the spectral properties of Anosov flows.

Provides a foundation for further analysis of dynamical resonances.

Abstract

We show that all generalized Pollicott-Ruelle resonant states of a topologically transitiv $C^\infty$-Anosov flow with an arbitrary $C^\infty$ potential, have full support.