# Propagation des singularit\'es et r\'esonances

## TL;DR

This paper refines the understanding of how singularities propagate in semiclassical resonances, linking resolvent estimates to trapped set dynamics, and improves analysis near the trapped set for resonance asymptotics.

## Contribution

It introduces a more precise connection between resolvent polynomial estimates and singularity propagation through the trapped set in semiclassical analysis.

## Key findings

- Enhanced understanding of singularity propagation in resonances
- Refined methods for analyzing the trapped set influence
- Successful application to asymptotic resonance analysis

## Abstract

In the framework of semiclassical resonances, we make more precise the link between polynomial estimates of the extension of the resolvent and propagation of the singularities through the trapped set. This approach makes it possible to eliminate infinity and to concentrate the study near the trapped set. It has allowed us in previous papers to obtain the asymptotic of resonances in various geometric situations.