Summary: Ann. Henri Poincar´e 99 (9999), 1­65
1424-0637/99000-0, DOI 10.1007/s00023-003-0000
c 2009 Birkh¨auser Verlag Basel/Switzerland Annales Henri Poincar´e
Patterson-Sullivan Distributions
and Quantum Ergodicity
Nalini Anantharaman and Steve Zelditch
Abstract. This article gives relations between two types of phase space dis-
tributions associated to eigenfunctions irj of the Laplacian on a compact
hyperbolic surface X:
· Wigner distributions
R
SX
a dWirj = Op(a)irj , irj L2(X), which
arise in quantum chaos. They are invariant under the wave group.
· Patterson-Sullivan distributions PSirj , which are the residues of the
dynamical zeta-functions Z(s; a) :=
P

e-sL
1-e-L

Source: Anantharaman, Nalini - Centre de Mathématiques Laurent Schwartz, École Polytechnique

Collections: Mathematics