Analytic continuation of the resolvent of the Laplacian and the dynamical zeta function

DOI10.2140/apde.2010.3.427zbMath1251.37031arXiv0906.0293OpenAlexW2065847142MaRDI QIDQ5894269

Vesselin Petkov, Latchezar Stoyanov

Publication date: 15 September 2011

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris, Analysis \& PDE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0906.0293

zbMATH Keywords

zeta functionsymbolic dynamicsopen billiardRuelle operatorcut-off resolventbilliard flowperiodic raysdistribution of resonanceslocal energy derayperiodic reflecting waystrapping obstacles

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Scattering theory for PDEs (35P25) Asymptotic distributions of eigenvalues in context of PDEs (35P20) General theory of partial differential operators (47F05) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30)

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Cites Work

• Singular perturbation of symbolic flows and poles of the zeta functions
• Decay of solutions of the wave equation in the exterior of several convex bodies
• On decay of correlations in Anosov flows
• Spectrum of the Ruelle operator and exponential decay of correlations for open billiard flows
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