Unique Ergodicity of Harmonic Currents on Singular Foliations of P2

Details Unique Ergodicity of Harmonic Currents on Singular Foliations of P2 Unique Ergodicity of Harmonic Currents on Singular Foliations of P2

2006-06-29

arxiv.org/abs/math/0606744v2

Mathematics

Dynamical Systems

Improved exposition

Scientific paper

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 $T.$

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