Abstract
Let ƒ be a dominating meromorphic self-map of a compact Kähler manifold. Assume that the topological degree of ƒ is larger than the other dynamical degrees. We give estimates of the dimension of the equilibrium measure of ƒ, which involve the Lyapounov exponents.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Références
Berteloot, F. and Dupont, C. Une caractérisation des exemples de Lattès de ℙk par leur mesure de Green, à paraître dansComment. Math. Helv.
Berteloot, F. and Mayer, V. Rudiments de dynamique holomorphe,Cours Spécialisés, 7, SMF et EDP Sciences, (2001).
Binder, I. and DeMarco, L. Dimension of pluriharmonic measure and polynomial endomorphisms ofC n,Int. Math. Res. Not.,11, 613–625, (2003).
Briend, J.Y. Exposants de Liapounoff et points périodiques d’endomorphismes holomorphes de ℂℙk, Thèse de doctorat de l’Université Paul Sabatier, Toulouse, (1997).
Briend, J.Y. and Duval, J. Exposants de Liapounoff et distribution des points périodiques d’un endomorphisme de ℂℙk,Acta Math.,182(2), 143–157, (1999).
Cornfeld, I.P., Fomin, S.V., and Sinaï, Ya.B.Ergodic Theory, Grand. Math. Wiss., No.245, Springer, (1985).
Dinh, T.C. and Sibony, N. Dynamique des applications d’allure polynomiale,J. Math. Pures Appl, (9),82(4), 367–423, (2003).
Dinh, T.C. and Sibony, N. Distributions des valeurs de transformations méromorphes et applications, arxiv.org/abs/math.DS/0306095, (2003).
Dinh, T.C. and Sibony, N. Regularization of currents and entropy, à paraître dansAnn. Sci. École Norm. Sup.
Dupont, C. Formule de Pesin et applications méromorphes, prépublication, (2004).
Falconer, K.Techniques in Fractal Geometry, John Wiley & Sons, (1997).
Guedj, V. Ergodic properties of rational mappings with large topological degree, à paraître dansAnn. Math.
Hironaka, H. Desingularization of complex analytic varieties,Actes Congrès Intern. Math., Tome 2, 627–631, (1970).
Katok, A. and Hasselblatt, B.Introduction to the Modern Theory of Dynamical Systems, Cambridge University Press, (1995).
Ledrappier, F. Quelques propriétés ergodiques des applications rationnelles,C.R. Acad. Sci. Paris Sér. I Math.,299(1), 37–40, (1984).
Lojasiewicz, S.Introduction to Complex Analytic Geometry, Birkhäuser, (1991).
Mañé, R. The Hausdorff dimension of invariant probabilities of rational maps,Lecture Notes in Math.,1331, Springer, (1988).
Pesin, Y.B. Dimension theory in dynamical systems,Chicago Lectures in Math. Series, (1997).
Ruelle, D. Ergodic theory of differentiable dynamical systems,Inst. Hautes Études Sci. Publ. Math.,50, 27–58, (1979).
Russakovskii, A. and Shiftman, B. Value distribution for sequences of rational mappings and complex dynamics,Ind. Univ. Math. J.,46, 897–932, (1997).
Sibony, N. Dynamique des applications rationnelles de ℙk, inDynamique et Géométrie Complexes, Panoramas et Synthèses, No. 8, SMF et EDP Sciences, (1999).
Young, L.S. Dimension, entropy and Lyapounov exponents,Ergodic Theory and Dynamical Systems,2(1), 109–124, (1982).
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Steven Krantz
Rights and permissions
About this article
Cite this article
Dinh, TC., Dupont, C. Dimension de la mesure d’équilibre d’applications méromorphes. J Geom Anal 14, 613–627 (2004). https://doi.org/10.1007/BF02922172
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02922172