Regular decay of ball diameters and spectra of Ruelle operators for\n contact Anosov flows

2011/04/05 by Luchezar Stoyanov, Stoyanov, Luchezar
Mathematics · Physics and Astronomy · #37D20 #37D25 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1104.0732

openalex publication_date 2011/04/05 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

For Anosov flows on compact Riemann manifolds we study the rate of decay\nalong the flow of diameters of balls B^s(x, ep) on local stable manifolds at\nLyapunov regular points x. We prove that this decay rate is similar for all\nsufficiently small values of \ε > 0. From this and the main result in\n citekn:St1, we derive strong spectral estimates for Ruelle transfer\noperators for contact Anosov flows with Lipschitz local stable holonomy maps.\nThese apply in particular to geodesic flows on compact locally symmetric\nmanifolds of strictly negative curvature. As is now well known, such spectral\nestimates have deep implications in some related areas, e.g. in studying\nanalytic properties of Ruelle zeta functions and partial differential\noperators, asymptotics of closed orbit counting functions, etc.\n

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