2005/05/03 by Carlangelo Liverani, Liverani, Carlangelo
Mathematics · Physics and Astronomy · #37C30 #37D20 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS #msc:37C30 #msc:37D20
paper · pdf · doi:10.48550/arxiv.math/0505049
arxiv created 2005/05/03 · openalex publication_date 2005/05/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
I show that the dynamical determinant, associated to an Anosov diffeomorphism, is the Fredholm determinant of the corresponding Ruelle-Perron-Frobenius transfer operator acting on appropriate Banach spaces. As a consequence it follows, for example, that the zeroes of the dynamical determinant describe the eigenvalues of the transfer operator and the Ruelle resonances and that, for \Co^∞ Anosov diffeomorphisms, the dynamical determinant is an entire function.