Bound on the number of Ruelle resonances for Gevrey hyperbolic flows
Malo J\'ez\'equel
TL;DR
This paper improves upper bounds on the number of Ruelle resonances for Gevrey hyperbolic flows by analyzing open hyperbolic maps instead of the flow directly.
Contribution
It introduces a new approach based on dynamical determinants and hyperbolic maps to tighten bounds on Ruelle resonances.
Findings
Established improved upper bounds for Ruelle resonances in large disks.
Applied Rugh's dynamical determinants approach to hyperbolic flows.
Replaced flow analysis with open hyperbolic maps for better estimates.
Abstract
We improve the best known upper bounds on the number of Ruelle resonances in disks of large radius for Gevrey uniformly hyperbolic flows. The proof is based on Rugh's approach of dynamical determinants that replaces the study of the flow itself by the analysis of a system of open hyperbolic maps.
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