Dynamique des applications d'allure polynomiale

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dc.creatorDinh, T. C.
dc.creatorSibony, N.
dc.date2002-11-18
dc.date.accessioned2026-07-07T04:53:02Z
dc.date.available2026-07-07T04:53:02Z
dc.descriptionWe 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 μsupported on $\bigcap_{n\geq 0}f^{-n}(V)$ satisfying the following properties. 1. The measure μis invariant, K-mixing, of maximal entropy \log d_t. 2. If J is the Jacobian of f with respect to a volume form then $\int \log J \d μ\geq \log d_t$. 3. For every probability measure νon V with no mass on pluripolar sets $d_t^{-n} (f^n)^*ν$ converges to $μ$. 4. If the p.s.h. functions on V are μ-integrables (μis PLB) then (a) The Lyapounov exponents for μare strictly positive. (b) μis exponentially mixing. (c) There is a proper analytic subset E of V such that for $z\not\in\E$, $μ^z_n:=d_t^{-n} (f^n)^*δ_z$ converges to μ. (d) The measure μis a limit of Dirac masses on the repelling periodic points. The condition μis PLB is stable under small pertubation of f. This gives large families where it is satisfied.
dc.description61 pages, nouvelle version
dc.identifierhttps://arxiv.org/abs/math/0211271
dc.identifierhttp://arxiv.org/abs/math/0211271
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/65693
dc.subjectDynamical Systems
dc.titleDynamique des applications d'allure polynomiale
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