# Semiclassical limits of distorted plane waves in chaotic scattering without a pressure condition

## TL;DR

This paper investigates the semi-classical behavior of distorted plane waves on certain manifolds, establishing boundedness, unique measures, and norm bounds without relying on a pressure condition.

## Contribution

It provides new results on the semi-classical limits of distorted plane waves in non-positive curvature manifolds without the pressure condition assumption.

## Key findings

- Distorted plane waves are bounded in $L^2_{loc}$ independently of $h$.
- They admit a unique semiclassical measure.
- Bounds on their $L^p_{loc}$ norms are established.

## Abstract

In this paper, we study the semi-classical behavior of distorted plane waves, on manifolds that are Euclidean near infinity or hyperbolic near infinity, and of non-positive curvature. Assuming that there is a strip without resonances below the real axis, we show that distorted plane waves are bounded in $L^2_{loc}$ independently of $h$, that they admit a unique semiclassical measure, and we prove bounds on their $L^p_{loc}$ norms.