Unique Ergodicity of Harmonic Currents on Singular Foliations of P2

Abstract

Let F be a holomorphic foliation of P^2 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. We also study the harmonic flow associated to the current $T.$

arXiv commentImproved exposition

References in corpus (1)

• Random conformal dynamical systems

Cited by in corpus (2)

• Rigidity of Julia sets for Henon type maps
• Statistical Behaviour of the Leaves of Riccati Foliations