Geodesic
Regularized Trace of the Perturbed Laplace--Beltrami Operator on Two-Dimensional Manifolds with Closed Geodesics
Matematičeskie zametki, Tome 93 (2013) no. 3, pp. 373-389

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The main result of the paper is the determination of the regularized trace of the Laplace–Beltrami operator with potential on the manifold given by a function family of smooth almost Liouville metrics on the sphere (besides, all the geodesics of these metrics are closed and have equal length).
Keywords: Laplace–Beltrami operator, almost Liouville metric, two-dimensional manifold, geodesic, sphero-conical coordinates, metric, pseudodifferential operator, bundle of half-densities, Hamiltonian flow, Dirichlet series
Mots-clés : cotangent space. 
@article{MZM_2013_93_3_a5,
     author = {T. V. Zykova},
     title = {Regularized {Trace} of the {Perturbed} {Laplace--Beltrami} {Operator} on {Two-Dimensional} {Manifolds} with {Closed} {Geodesics}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {373--389},
     publisher = {mathdoc},
     volume = {93},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_93_3_a5/}
}
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T. V. Zykova. Regularized Trace of the Perturbed Laplace--Beltrami Operator on Two-Dimensional Manifolds with Closed Geodesics. Matematičeskie zametki, Tome 93 (2013) no. 3, pp. 373-389. http://geodesic.mathdoc.fr/item/MZM_2013_93_3_a5/