1205.5458 (Yuri A. Kordyukov)

Classical and quantum ergodicity on orbifolds    [PDF]

Yuri A. Kordyukov

We extend to orbifolds classical results on quantum ergodicity due to Shnirelman, Colin de Verdi\`ere 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.

View original: http://arxiv.org/abs/1205.5458