# Spectral analysis of morse-smale flows ii: resonances and resonant states

## TL;DR

This paper explicitly computes the correlation spectrum of Morse-Smale flows, linking eigenvalues to flow topology, Lyapunov exponents, and monodromy, and derives sharp Weyl asymptotics for dynamical resonances.

## Contribution

It provides an explicit spectral analysis of Morse-Smale flows, connecting eigenvalues with flow topology and Lyapunov exponents, and establishes Weyl asymptotics for resonances.

## Key findings

- Eigenvalues form vertical bands in the presence of periodic orbits
- Explicit correlation spectrum in terms of flow invariants
- Sharp Weyl asymptotics for dynamical resonances

## Abstract

The goal of the present work is to compute explicitely the correlation spectrum of a Morse-Smale flow in terms of the Lyapunov exponents of the Morse--Smale flow, the topology of the flow around periodic orbits and the monodromy of some given flat connection. The corresponding eigenvalues exhibit vertical bands when the flow has periodic orbits. As a corollary, we obtain sharp Weyl asymptotics for the dynamical resonances.