The semiclassical zeta function for geodesic flows on negatively curved manifolds

2013/11/20 by Fréderic Faure, Faure, Frédéric, Masato Tsujii +1 · 1 citation
Mathematics · Physics and Astronomy · #37C30 #37D40 #53D25 #81Q50 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1311.4932

openalex publication_date 2013/11/20 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We consider the semi-classical (or Gutzwiller-Voros) zeta function for C^∞ contact Anosov flows. Analyzing the spectrum of transfer operators associated to the flow, we prove, for any τ>0, that its zeros are contained in the union of the τ-neighborhood of the imaginary axis, |\Re(s)|0 is the hyperbolicity exponent of the flow. Further we show that the zeros in the neighborhood of the imaginary axis satisfy an analogue of the Weyl law.

Cited by

• Can quantum dynamics emerge from classical chaos?

Related

• Anosov Flows and Dynamical Zeta Functions
• On cohomological theory of dynamical zeta functions
• Regular decay of ball diameters and spectra of Ruelle operators for\n contact Anosov flows
• Mayer Transfer Operator Approach to Selberg Zeta Function
• The Bowen\unicodex2013Series coding and zeros of zeta functions