Ruelle-Pollicott Resonances for Manifolds with Hyperbolic Cusps

TL;DR

This paper introduces new techniques to analyze the spectral properties of geodesic flows on negatively curved manifolds with hyperbolic cusps, advancing understanding of their dynamical systems.

Contribution

It develops novel methods to construct Ruelle-Pollicott spectra specifically for manifolds with hyperbolic cusps, extending previous spectral analysis techniques.

Findings

Successfully constructed Ruelle-Pollicott spectra for the specified manifolds

Enhanced understanding of geodesic flow dynamics on hyperbolic cusp manifolds

Provided new tools for spectral analysis in non-compact negatively curved spaces

Abstract

We present new methods to construct a Ruelle-Pollicott spectrum for the geodesic flow on manifolds with strictly negative curvature and a finite number of hyperbolic cusps.