Parabolic curves for diffeomorphisms in C2.
Parabolic curves in .
Points périodiques d’applications birationnelles de
Nous donnons une condition suffisante pour l’existence de points périodiques pour une application birationnelle de . Sous cette hypothèse, une estimation précise du nombre de points périodiques de période fixée est obtenue. Nous donnons une application de ce résultat à l’étude dynamique de ces applications, en calculant explicitement l’auto-intersection de leur courant invariant naturellement associé. Nos résultats reposent essentiellement sur le théorème de Bézout donnant le cardinal de l’intersection...
Polynomial diffeomorphisms of C2: currents, equilibrium measure and hyperbolicity.
Polynomial diffeomorphisms of C2. III. Ergodicity, exponents and entropy of the equilibrium measure.
Polynomial diffeomorphisms of C2. IV: The measure of maximal entropy and laminar currents.
Pull-back of currents by meromorphic maps
Let and be compact Kähler manifolds, and let be a dominant meromorphic map. Based upon a regularization theorem of Dinh and Sibony for DSH currents, we define a pullback operator for currents of bidegrees of finite order on (and thus foranycurrent, since is compact). This operator has good properties as may be expected. Our definition and results are compatible to those of various previous works of Meo, Russakovskii and Shiffman, Alessandrini and Bassanelli, Dinh and Sibony, and can...