Courants extrémaux et dynamique complexe
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 38 (2005) no. 3, pp. 407-426.
DOI: 10.1016/j.ansens.2005.02.001
Guedj, Vincent 1

1 Université Paul Sabatier, Laboratoire Emile Picard, UMR 5580, 118 route de Narbonne, 31062 TOULOUSE Cedex 04 (France)
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Guedj, Vincent. Courants extrémaux et dynamique complexe. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 38 (2005) no. 3, pp. 407-426. doi : 10.1016/j.ansens.2005.02.001. http://archive.numdam.org/articles/10.1016/j.ansens.2005.02.001/

[1] Bedford E., Lyubich M., Smillie J., Polynomial diffeomorphisms of C 2 . IV. The measure of maximal entropy and laminar currents, Invent. Math. 112 (1) (1993) 77-125. | MR | Zbl

[2] Bedford E., Smillie J., Polynomial diffeomorphisms of C 2 . III. Ergodicity, exponents and entropy of the equilibrium measure, Math. Ann. 294 (3) (1992) 395-420. | MR | Zbl

[3] Bedford E., Smillie J., Polynomial diffeomorphisms of C 2 . V. Critical points and Lyapunov exponents, J. Geom. Anal. 8 (3) (1998) 349-383. | MR | Zbl

[4] Bost J.-B., Gillet H., Soulé C., Heights of projective varieties and positive Green forms, J. Amer. Math. Soc. 7 (4) (1994) 903-1027. | MR | Zbl

[5] Cantat S., Dynamique des automorphismes des surfaces K3, Acta Math. 187 (1) (2001) 1-57. | MR | Zbl

[6] Coman D., Guedj V., Invariant currents and dynamical Lelong numbers, J. Geom. Anal. 14 (2) (2004) 199-213. | MR | Zbl

[7] Demailly J.-P., Courants positifs extrémaux et conjecture de Hodge, Invent. Math. 69 (3) (1982) 347-374. | MR | Zbl

[8] Demailly J.-P., Propagation des singularités des courants positifs fermés, Ark. Mat. 23 (1) (1985) 35-52. | MR | Zbl

[9] Demailly J.-P., Complex analytic and differential geometry, Free accessible book, http://www-fourier.ujf-grenoble.fr/~demailly/books.html.

[10] Diller J., Favre C., Dynamics of bimeromorphic maps of surfaces, Amer. J. Math. 123 (6) (2001) 1135-1169. | MR | Zbl

[11] Dinh T.C., Suites d'applications méromorphes multivaluées et courants laminaires, Prépublication, décembre 2003.

[12] Dinh T.C., Sibony N., Green currents for holomorphic automorphisms of compact Kähler manifolds, math.DS/0311322.

[13] Dujardin R., Laminar currents in P 2 , Math. Ann. 325 (4) (2003) 745-765. | MR | Zbl

[14] Fornæss J.-E., Sibony N., Complex Hénon mappings in C 2 and Fatou-Bieberbach domains, Duke Math. J. 65 (2) (1992) 345-380. | MR | Zbl

[15] Friedland S., Entropy of polynomial and rational maps, Ann. of Math. (2) 133 (2) (1991) 359-368. | MR | Zbl

[16] Griffiths P.-A., Harris J., Principles of Algebraic Geometry, Wiley, New York, 1978. | MR | Zbl

[17] Griffiths P.-A., King J., Nevanlinna theory and holomorphic mappings between algebraic varieties, Acta Math. 130 (1973) 145-220. | MR | Zbl

[18] Gromov M., On the entropy of holomorphic maps, Manuscrit, 1977.

[19] Guedj V., Dynamics of polynomial mappings of C 2 , Amer. J. Math. 124 (1) (2002) 75-106. | MR | Zbl

[20] Guedj V., Ergodic properties of rational mappings with large topological degree, Preprint, January 2003, à paraître in Annals of Mathematics. | MR | Zbl

[21] Guedj V., Sibony N., Dynamics of polynomial automorphisms of C k , Ark. Mat. 40 (2) (2002) 207-243. | MR | Zbl

[22] Guedj V., Zeriahi A., Intrinsic capacities on compact Kähler manifolds, math.CV/0401302.

[23] Harvey R., Holomorphic chains and their boundaries, in: Several Complex Variables (Proc. Sympos. Pure Math., vol. XXX, Part 1, Williams Coll., Williamstown, Mass., 1975), American Mathematical Society, Providence, RI, 1977, pp. 309-382. | MR | Zbl

[24] Huckleberry A., Subvarieties of homogeneous and almost homogeneous manifolds, in: Contributions to Complex Analysis and Analytic Geometry, Aspects Math., vol. E26, Vieweg, Braunschweig, 1994, pp. 189-232. | MR | Zbl

[25] Katok A., Hasselblatt B., Introduction to the Modern Theory of Dynamical Systems, with a supplementary chapter by Katok and Leonardo Mendoza, Encyclopedia of Mathematics and Its Applications, vol. 54, Cambridge University Press, Cambridge, 1995, xviii+802 pp. | MR | Zbl

[26] Lelong P., Intégration sur un ensemble analytique complexe, Bull. Soc. Math. France 85 (1957) 239-262. | Numdam | MR | Zbl

[27] Lelong P., Éléments extrémaux sur le cône des courants positifs fermés, in: Séminaire Pierre Lelong (Analyse), Année 1971-1972, Lecture Notes in Math., vol. 332, Springer, Berlin, 1973, pp. 112-131. | MR | Zbl

[28] Levine H., A theorem on holomorphic mappings into complex projective space, Ann. of Math. (2) 71 (1960) 529-535. | MR | Zbl

[29] Méo M., Image inverse d'un courant positif fermé par une application analytique surjective, C. R. Acad. Sci. Paris Sér. I Math. 322 (12) (1996) 1141-1144. | MR | Zbl

[30] Russakovskii A., Shiffman B., Value distribution for sequences of rational mappings and complex dynamics, Indiana Univ. Math. J. 46 (3) (1997) 897-932. | MR | Zbl

[31] Shiffman B., Applications of geometric measure theory to value distribution theory for meromorphic maps, in: Value Distribution Theory (Proc. Tulane Univ. Program, Tulane Univ., New Orleans, La., 1972-1973), Part A, Dekker, New York, 1974, pp. 63-95. | MR | Zbl

[32] Sibony N., Dynamique des applications rationnelles de P k , in : Dynamique et Géométrie Complexes, Panorama et Synthèses, 1999. | MR | Zbl

[33] Skoda H., Sous-ensembles analytiques d’ordre fini ou infini dans C n , Bull. Soc. Math. France 100 (1972) 353-408. | Numdam | MR | Zbl

[34] Sullivan D., Cycles for the dynamical study of foliated manifolds and complex manifolds, Invent. Math. 36 (1976) 225-255. | MR | Zbl

[35] Yomdin Y., Volume growth and entropy, Israel J. Math. 57 (3) (1987) 285-300. | MR | Zbl

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