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Pré-Publication, Document De Travail Année : 2023

Length orthospectrum and the correlation function on flat tori

Résumé

This note presents some of the results obtained in https://arxiv.org/pdf/2207.05410.pdf and it has been the object of a talk of the second author during the Journées “Équations aux Dérivées Partielles” (Obernai, june 2022). We study properties of geodesics that are orthogonal to two convex subsets of the flat torus. We discuss meromorphic properties of a geometric Epstein zeta function associated to the set of lengths of such orthogeodesics. We also define the associated length distribution and discuss singularities of its Fourier transform. Our analysis relies on a fine study of the dynamical correlation function of the geodesic flow on the torus and the definition of anisotropic Sobolev spaces that are well-adapted to this integrable dynamics.
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hal-03978454 , version 1 (08-02-2023)

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Nguyen Viet Dang, Matthieu Léautaud, Gabriel Rivière. Length orthospectrum and the correlation function on flat tori. 2023. ⟨hal-03978454⟩
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