arXiv Analytics

Sign in

arXiv:math/0606744 [math.DS]AbstractReferencesReviewsResources

Unique Ergodicity of Harmonic Currents on Singular Foliations of P2

John Erik Fornaess, Nessim Sibony

Published 2006-06-29, updated 2009-03-11Version 2

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 $T.$

Comments: Improved exposition
Categories: math.DS, math.CV
Subjects: 32S65, 57R30
Related articles: Most relevant | Search more
arXiv:2103.15513 [math.DS] (Published 2021-03-29)
Jacobian curve of singular foliations
arXiv:2301.04530 [math.DS] (Published 2023-01-11)
Action on the circle at infinity of foliations of ${\mathbb R}^2 $
arXiv:1208.2389 [math.DS] (Published 2012-08-12)
Random Orderings and Unique Ergodicity of Automorphism Groups

Links

Toolbox