November 24, 2007 (Saturday)
Room 517, Meng Wah
Complex, HKU
Professor Nessim Sibony
Université de Paris-Sud,
Dynamics of Holomorphic
foliations in CP2
Abstract
The goal is to describe
some global dynamical properties of polynomial vector fields in C2. It's more appropriate
to consider the extension as a holomorphic foliation in the complex projective
space P2. Let F be a holomorphic foliation of P2 by Riemann surfaces. Assume all the
singular points of F are hyperbolic. If
F has no algebraic leaf, then there
is a unique positive harmonic (1, 1) current T of mass one,
directed by F. This implies
strong ergodic properties for the foliation F. This is joint work with J.E. FORNAESS.