Classical and quantum ergodicity on orbifolds

Yuri A. Kordyukov

doi:10.1134/s1061920812030041

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arXiv · 1205.5458

Classical and quantum ergodicity on orbifolds

Yuri A. Kordyukov

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Abstract

We extend to orbifolds classical results on quantum ergodicity due to Shnirelman, Colin de Verdière and Zelditch, proving that, for any positive, first-order self-adjoint elliptic pseudodifferential operator P on a compact orbifold X with positive principal symbol p, ergodicity of the Hamiltonian flow of p implies quantum ergodicity for the operator P. We also prove ergodicity of the geodesic flow on a compact Riemannian orbifold of negative sectional curvature.

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BibTeX RIS

Yuri A. Kordyukov. 2012-05-24. Classical and quantum ergodicity on orbifolds. https://doi.org/10.1134/s1061920812030041

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