Mathematics – Dynamical Systems
Scientific paper
2002-11-18
Mathematics
Dynamical Systems
61 pages, nouvelle version
Scientific paper
We study the dynamics of polynomial-like mappings in several variables. A special case of our results is the following theorem. Let f be a proper holomorphic map from an open set U onto a Stein manifold V, $U\subset\subset V$. Assume f is of topological degree d_t>1. Then there is a probability measure \mu supported on $\bigcap_{n\geq 0}f^{-n}(V)$ satisfying the following properties. 1. The measure \mu is invariant, K-mixing, of maximal entropy \log d_t. 2. If J is the Jacobian of f with respect to a volume form then $\int \log J \d \mu \geq \log d_t$. 3. For every probability measure \nu on V with no mass on pluripolar sets $d_t^{-n} (f^n)^*\nu$ converges to $\mu$. 4. If the p.s.h. functions on V are \mu-integrables (\mu is PLB) then (a) The Lyapounov exponents for \mu are strictly positive. (b) \mu is exponentially mixing. (c) There is a proper analytic subset E of V such that for $z\not\in\E$, $\mu^z_n:=d_t^{-n} (f^n)^*\delta_z$ converges to \mu. (d) The measure \mu is a limit of Dirac masses on the repelling periodic points. The condition \mu is PLB is stable under small pertubation of f. This gives large families where it is satisfied.
Dinh Tien-Cuong
Sibony Nessim
No associations
LandOfFree
Dynamique des applications d'allure polynomiale does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Dynamique des applications d'allure polynomiale, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dynamique des applications d'allure polynomiale will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-508943