Steve Zelditch
Published 2000-02-03Version 1
This paper contains a very simple and general proof that eigenfunctions of quantizations of classically ergodic systems become uniformly distributed in phase space. This ergodicity property of eigenfunctions f is shown to follow from a convexity inequality for the invariant states (Af,f). This proof of ergodicity of eigenfunctions simplifies previous proofs (due to A.I. Shnirelman, Colin de Verdiere and the author) and extends the result to the much more general framework of C* dynamical systems.
Comments: Only very minor differences with the published version
Journal: Comm. Math. Phys. 177 (1996), no. 2, 507--528
On the geometry of twisted prolongations, and dynamical systems
Application of chaos degree to some dynamical systems
Lambda-symmetries of Dynamical Systems, Hamiltonian and Lagrangian equations
