Flat trace estimates for Anosov flows
Long Jin, Zhongkai Tao
TL;DR
This paper establishes a high energy flat trace estimate for the modified resolvent of Anosov flow generators, addressing a key gap in the local trace formula proof and aiding its extension to Axiom A flows.
Contribution
It provides a crucial high energy estimate that completes the proof of the local trace formula for Anosov flows, facilitating generalization to Axiom A flows.
Findings
Proves a high energy flat trace estimate for Anosov flows
Completes the proof of the local trace formula in this setting
Supports ongoing generalization to Axiom A flows
Abstract
We prove a high energy flat trace estimate for the modified resolvent of the generator of an Anosov flow. This fills a gap in the proof of the local trace formula in [Jin-Zworski '17] and is a by-product of the authors' ongoing project of its generalization to Axiom A flows.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Quantum chaos and dynamical systems · Advanced Differential Equations and Dynamical Systems