Mathematics – Dynamical Systems
Scientific paper
2010-04-22
Mathematics
Dynamical Systems
44 pages
Scientific paper
We introduce the heat equation relative to a positive dd-bar-closed current and apply it to the invariant currents associated with Riemann surface laminations possibly with singularities. The main examples are holomorphic foliations by Riemann surfaces in projective spaces. We prove two kinds of ergodic theorems for such currents: one associated to the heat diffusion and one close to Birkhoff's averaging on orbits of a dynamical system. The heat diffusion theorem with respect to a harmonic measure is also developed for real laminations.
Dinh Tien-Cuong
Nguyen Viet-Anh
Sibony Nessim
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