# Horocyclic invariance of Ruelle resonant states for contact Anosov flows in dimension 3

## TL;DR

This paper proves that for smooth contact Anosov flows in three dimensions, the first band of Ruelle resonant states are distributions annihilated by the unstable derivative, revealing a new invariance property.

## Contribution

It establishes the horocyclic invariance of Ruelle resonant states for contact Anosov flows in dimension three, a novel result in dynamical systems theory.

## Key findings

- Resonant states are distributions killed by the unstable derivative.
- First band of Ruelle resonances exhibits horocyclic invariance.
- Provides new insights into the structure of Ruelle resonances in 3D contact flows.

## Abstract

We show that for smooth contact Anosov flows in dimension 3, the resonant states associated to the first band of Ruelle resonances are distributions that are killed by the unstable derivative.