Dynamique des automorphismes des surfaces K3

Acta Mathematica

Volumn 187, Issue 1, 2001, Pages 1-57

  Cantat, Serge ^a,b  

^a UNIVERSITÉ DE RENNES 1   (France)

^b CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040489280     PISSN: 00015962     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02392831     Document Type: Article

References (49)

1. BARTH, W., PETERS, C. & VAN DE VEN, A., Compact Complex Surfaces. Ergeb. Math. Grenzgeb. (3), 4. Springer-Verlag, Berlin-New York, 1984.
2. 2. Invent. Math., 114 (1993), 277-288.
3. 2, IV. The measure of maximal entropy and laminar currents. Invent. Math., 112 (1993), 77-125.
4. 2, III. Ergodicity, exponents and entropy of the equilibrium measure. Math. Ann., 294 (1992), 395-420.
5. BRUNELLA, M., Courbes entières et feuilletages holomorphes. Enseign. Math. (2), 45 (1999), 195-216.
6. CANTAT, S., Dynamique des automorphismes des surfaces complexes compactes. Thèse de doctorat de l'É.N.S.-Lyon, 1999.
7. _ Dynamique des automorphismes des surfaces projectives complexes. C. R. Acad. Sci. Paris Sér. I Math., 328 (1999), 901-906.
8. _ Sur la dynamique du groupe d'automorphismes des surfaces K3. À paraître dans Transform. Groups, 2001.
9. DEMAILLY, J.-P., Courants positifs extrémaux et conjecture de Hodge. Invent. Math., 69 (1982), 347-374.
10. _ Variétés hyperboliques et équations différentielles algébriques. Gaz. Math., 73 (1997), 3-23.
11. 0 avec champs de vecteurs. C. R. Acad. Sci. Paris Sér. I Math., 329 (1999), 409-412.
12. DOUADY, A., Prolongement de mouvements holomorphes (d'après Słodkowski et autres), dans Séminaire Bourbaki, vol. 1993/94, exp. n° 775. Astérisque, 227 (1995), 7-20.
13. ERËMENKO, A. È. & LYUBICH, M. YU., The dynamics of analytic transformations. Algebra i Analiz, 1:3 (1989), 1-70 (Russian); English translation in Leningrad Math . J., 1 (1990), 563-634.
14. ERËMENKO, A. È. & LYUBICH, M. YU., The dynamics of analytic transformations. Algebra i Analiz, 1:3 (1989), 1-70 (Russian); English translation in Leningrad Math . J., 1 (1990), 563-634.
15. FUJIKI, A., On automorphism groups of compact Kähler manifolds. Invent. Math., 44 (1978), 225-258.
16. GHYS, É., Holomorphic Anosov systems. Invent. Math., 119 (1995), 585-614.
17. _ Laminations par surfaces de Riemann, dans Dynamique et géométrie complexes (Lyon, 1997), pp. 49-95. Panor. Synthèses, 8. Soc. Math. France, Paris, 1999.
18. _ Laminations par surfaces de Riemann, dans Dynamique et géométrie complexes (Lyon, 1997), pp. 49-95. Panor. Synthèses, 8. Soc. Math. France, Paris, 1999.
19. GHYS, É. & VERJOVSKY, A., Locally free holomorphic actions of the complex affine group, in Geometric Study of Foliations (Tokyo, 1993), pp. 201-217. World Sci. Publishing, River Edge, NJ, 1994.
20. GRIFFITHS, P. & HARRIS, J., Principles of Algebraic Geometry (reprint of the 1978 original). Wiley Classics Library, John Wiley & Sons, New York, 1994.
21. GROMOV, M., On the entropy of holomorphic map. Manuscrit, 1980.
22. n. Indiana Univ. Math. J., 43 (1994), 321-365.
23. HURDER, S. & MITSUMATSU, Y., Transverse Euler classes of foliations on nonatomic foliation cycles, in Differential Topology, Foliations, and Group Actions (Rio de Janeiro, 1992), pp. 29-39. Contemp. Math., 161. Amer. Math. Soc., Providence, RI, 1994.
24. HURDER, S. & MITSUMATSU, Y., Transverse Euler classes of foliations on nonatomic foliation cycles, in Differential Topology, Foliations, and Group Actions (Rio de Janeiro, 1992), pp. 29-39. Contemp. Math., 161. Amer. Math. Soc., Providence, RI, 1994.
25. KATOK, A., Lyapunov exponents, entropy and periodic orbits for diffeomorphisms. Inst. Hautes Études Sci. Publ. Math., 51 (1980), 137-173.
26. KATOK, A. & HASSELBLATT, B., Introduction to the Modern Theory of Dynamical Systems. With a supplement by Anatole Katok and Leonardo Mendoza. Encyclopedia Math. Appl., 54. Cambridge Univ. Press, Cambridge, 1995.
27. KEUM, J. H., Every algebraic Kummer surface is the K3-cover of an Enriques surface. Nagoya Math. J., 118 (1990), 99-110.
28. LAMARI, A., Le cône kählérien d'une surface. J. Math. Pures Appl. (9), 78 (1999), 249-263.
29. LANG, S., Introduction to Complex Hyperbolic Spaces. Springer-Verlag, New York, 1987.
30. LAUFER, H. B., Normal Two-Dimensional Singularities. Ann. of Math. Stud., 71. Princeton Univ. Press, Princeton, NJ, 1971.
31. LEDRAPPIER, F., Some properties of absolutely continuous invariant measures on an interval. Ergodic Theory Dynamical Systems, 1 (1981), 77-93.
32. LELONG, P., Éléments extrémaux sur le cône des courants positifs fermés, dans Séminaire Pierre Lelong (Analyse), Année 1971-1972, pp. 112-131. Lecture Notes in Math., 332. Springer-Verlag, Berlin, 1973.
33. LELONG, P., Éléments extrémaux sur le cône des courants positifs fermés, dans Séminaire Pierre Lelong (Analyse), Année 1971-1972, pp. 112-131. Lecture Notes in Math., 332. Springer-Verlag, Berlin, 1973.
34. MAZUR, B., The topology of rational points. Experiment. Math., 1 (1992), 35-45.
35. NEVANLINNA, R., Analytic Functions. Grundlehren Math. Wiss., 162. Springer-Verlag, New York-Berlin, 1970.
36. NEWHOUSE, S. E., Entropy in smooth dynamical systems, in Proceedings of the International Congress of Mathematicians, Vol. II (Kyoto, 1990), pp. 1285-1294. Math. Soc. Japan, Tokyo, 1991.
37. NIKULIN, V. V., Quotient-groups of groups of automorphisms of hyperbolic forms by subgroups generated by 2-reflections. Algebro-geometric applications, in Current Problems in Mathematics, Vol. 18, pp. 3-114. Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Informatsii, Moscow, 1981.
38. ORNSTEIN, D. S. & WEISS, B., Statistical properties of chaotic systems. Bull. Amer. Math. Soc. (N.S.), 24 (1991), 11-116.
39. PJATECKIǏ-ŠAPIRO, I. I. & ŠAFAREVIČ, I. R., Torelli's theorem for algebraic surfaces of type K3. Izv. Akad. Nauk SSSR Ser. Mat., 35 (1971), 530-572 (Russian).
40. SÉMINAIRE PALAISEAU 1981/1982, Géométrie des surfaces K3 : modules et périodes. Astérisque, 126. Soc. Math. France, Paris, 1985.
41. k, dans Dynamique et géométrie complexes (Lyon, 1997), pp. 97-185. Panor. Synthèses, 8. Soc. Math. France, Paris, 1999.
42. k, dans Dynamique et géométrie complexes (Lyon, 1997), pp. 97-185. Panor. Synthèses, 8. Soc. Math. France, Paris, 1999.
43. SULLIVAN, D., Cycles for the dynamical study of foliated manifolds and complex manifolds. Invent. Math., 36 (1976), 225-255.
44. THURSTON, W., The Geometry and Topology of 3-Manifolds. Princeton Univ. Lecture Notes, Princeton, NJ, 1977.
45. TROYANOV, M., Les surfaces euclidiennes à singularités coniques. Enseign. Math. (2), 32 (1986), 79-94.
46. 1, in Recent Developments in the Inverse Galois Problem (Seattle, WA, 1993), pp. 273-289. Contemp. Math., 186. Amer. Math. Soc., Providence, RI, 1995.
47. 1, in Recent Developments in the Inverse Galois Problem (Seattle, WA, 1993), pp. 273-289. Contemp. Math., 186. Amer. Math. Soc., Providence, RI, 1995.
48. WU, H., Complex stable manifolds of holomorphic diffeomorphisms. Indiana Univ. Math. J., 42 (1993), 1349-1358.
49. YOMDIN, Y., Volume growth and entropy. Israel J. Math., 57 (1987), 285-300.