Green currents for holomorphic automorphisms of compact kahler manifolds

Journal of the American Mathematical Society

Volumn 18, Issue 2, 2005, Pages 291-312

  Dinh, Tien Cuong ^a   Sibony, Nessim ^a  

^a UNIVERSITÉ PARIS SUD   (France)

Author keywords

Equilibrium measure; Green current; Mixing

Indexed keywords

EID: 18144384409     PISSN: 08940347     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0894-0347-04-00474-6     Document Type: Article

References (38)

1. 2 IV: The measure of maximal entropy and laminar currents, Invent. Math., 112 (1993), 77-125. MR1207478 (94g:32035)
2. 2 III: Ergodicity, exponents and entropy of the equilibrium measure, Math. Ann., 294 (1992), 395-420. MR1188127 (93k:32062)
3. A. Blanchard, Sur les variétés analytiques complexes, Ann. Sci. Ecole Norm. Sup. (3), 73 (1956), 157-202. MR0087184 (19:316e)
4. J.-B. Bost, H. Gillet, C. Soulé, Heights of projective varieties and positive Green forms, J. Amer. Math. Soc., 7 (1994), no. 4, 903-1027. MR1260106 (95j:14025)
5. k(ℂ), IHES Publ. Math., 93 (2001), 145-159. MR1863737 (2002k:32027)
6. S. Cantat, Dynamique des automorphismes des surfaces K3, Acta Math., 187 (2001), no. 1, 1-57. MR1864630 (2003h:32026)
7. L. Clozel and E. Ullmo, Correspondances modulaires et mesures invariantes, J. reine angew. Math., 558 (2003), 47-83. MR1979182
8. J.P. Demailly, Monge-Ampère Operators, Lelong numbers and Intersection theory in Complex Analysis and Geometry, Plenum Press (1993), 115-193 (V. Ancona and A. Silva editors). MR1211880 (94k:32009)
9. J.P. Demailly, Introduction à la théorie de Hodge, Panoramas and Synthèses, 3 (1996), 1-111. MR1409819
10. J.P. Demailly, Pseudoconvex-concave duality and regularization of currents. Several complex variables (Berkeley, CA, 1995-1996), 233-271, Math. Sci. Res. Inst. Publ., 37, Cambridge Univ. Press, Cambridge, 1999. MR1748605 (2002e:32046)
11. T. C. Dinh, Distribution des préimages et des points périodiques d'une correspondance polynomiale, Bull. Soc. Math. France, to appear.
12. T. C. Dinh, Suites d'applications méromorphes multivaluées et courants laminaires, preprint, 2003. arXiv:math.DS/0309421.
13. T.C. Dinh and N. Sibony, Dynamique des applications d'allure polynomiale, Journal de Math. Pures et Appl., 82 (2003), 367-423. MR1992375 (2004e:37063)
14. T.C. Dinh and N. Sibony, Dynamique des applications polynomials semi-régulières, Arkiv för Matematik, 42 (2004), 61-85. MR2056545
15. T.C. Dinh and N. Sibony, Groupes commutatifs d'automorphismes d'une variété kählérienne compacte, Duke Math. J., 123 (2004), no. 2, 311-328. MR2066940
16. T.C. Dinh and N. Sibony, Distribution de valeurs d'une suite de transformations méromorphes et applications, preprint, 2003. arXiv:math.DS/0306095.
17. T.C. Dinh and N. Sibony, Une borne supérieure de l'entropie topologique d'une application rationnelle, Ann. of Math., to appear.
18. T.C. Dinh and N. Sibony, Regularization of currents and entropy, Ann. Sci. Ecole Norm. Sup., to appear.
19. k, J. Funct. Anal., to appear.
20. T. C. Dinh and N. Sibony, Decay of correlations and central limit theorem for meromorphic maps, preprint, 2004. arXiv:math.DS/0410008.
21. C. Favre and V. Guedj, Dynamique des applications rationnelles des espaces multiprojectifs, Indiana Univ. Math. J., 50 (2001), no. 2, 881-934. MR1871393 (2002m:32024)
22. k and Fatou-Biebebach domains, Duke Math. J., 65 (1992), 245-250. MR1150591 (93d:32040)
23. J.E. Fornæss and N. Sibony, Complex dynamics in higher dimension, in Complex potential theory (Montréal, PQ, 1993), Nato ASI series Math, and Phys. Sci., vol. C439, Kluwer (1994), 131-186. MR1332961 (96k:32057)
24. H. Gillet and C. Soulé, Arithmetic intersection theory, I.H.E.S. Publ. Math., 72 (1990), 93-174 (1991). MR1087394 (92d:14016)
25. P. Griffiths and J. Harris, Principles of algebraic geometry, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1994. MR1288523 (95d:14001)
26. M. Gromov, On the entropy of holomorphic maps, Enseignement Math., 49 (2003), 217-235 (manuscript, 1977). MR2026895
27. M. Gromov, Convex sets and Kähler manifolds, Advances in differential geometry and topology, Word Sci. Publishing, Teaneck, NJ, 1998, 1-38. MR1095529 (92d:52018)
28. 2, Amer. J. Math., 124 (2002), no. 1, 75-106. MR1879000 (2003b:32021)
29. V. Guedj, Ergodic properties of rational mappings with large topological degree, Ann. of Math., to appear.
30. k, Arkiv för Matematik, 40 (2002), 207-243. MR1948064 (2004b:32029)
31. A. Khovanskii, Fewnomials and Pfaff manifolds, I.C.M. 1983, Warsawa (1984), 549-565. MR0804711 (87d:58014)
32. G. A. Margulis, Discrete subgroups of semisimple Lie groups, Springer-Verlag, 1991. MR1090825 (92h:22021)
33. B. Mazur, The topology of rational points, Experiment Math., 1 (1992), 35-45. MR1181085 (93j:14020)
34. C. T. McMullen, Dynamics on K3 surfaces: Salem numbers and Siegel disks, J. reine angew. Math., 545 (2002), 201-233. MR1896103 (2003a:37057)
35. k, Panoramas et Synthèses, 8 (1999), 97-185. MR1760844 (2001e:32026)
36. B. Tessier, Bonnesen-type inequalities in algebraic geometry, Sem. on Diff. Geom. (1982), 85-105. Princeton Univ. Press. MR0645731 (83d:52010)
37. C. Voisin, Intrinsic pseudovolume forms and K-correspondences, preprint, 2003, arXiv:math.AG/0212110.
38. Y. Yomdin, Volume growth and entropy, Israel J. Math., 57 (1987), 285-300. MR0889979 (90g:58008)