@article{PMIHES_2007__105__49_0, author = {McMullen, Curtis T.}, title = {Dynamics on blowups of the projective plane}, journal = {Publications Math\'ematiques de l'IH\'ES}, pages = {49--89}, publisher = {Springer}, volume = {105}, year = {2007}, doi = {10.1007/s10240-007-0004-x}, mrnumber = {2354205}, language = {en}, url = {http://archive.numdam.org/articles/10.1007/s10240-007-0004-x/} }
TY - JOUR AU - McMullen, Curtis T. TI - Dynamics on blowups of the projective plane JO - Publications Mathématiques de l'IHÉS PY - 2007 SP - 49 EP - 89 VL - 105 PB - Springer UR - http://archive.numdam.org/articles/10.1007/s10240-007-0004-x/ DO - 10.1007/s10240-007-0004-x LA - en ID - PMIHES_2007__105__49_0 ER -
McMullen, Curtis T. Dynamics on blowups of the projective plane. Publications Mathématiques de l'IHÉS, Tome 105 (2007), pp. 49-89. doi : 10.1007/s10240-007-0004-x. http://archive.numdam.org/articles/10.1007/s10240-007-0004-x/
1. A Lefschetz fixed point formula for elliptic complexes II, Ann. Math., 88 (1968), 451-491 | MR | Zbl
, ,2. Global behavior of the solutions of Lyness' difference equation u n+2 u n =u n+1+a , J. Difference Equ. Appl., 10 (2004), 977-1003 | Zbl
, ,3. E. Bedford and K. Kim, Dynamics of rational surface automorphisms: Linear fractional recurrences, Preprint, 2006.
4. E. Bedford and K. Kim, Periodicities in linear fractional recurrences: Degree growth of birational surface maps, Preprint, 2005. | MR
5. Energy and invariant measures for birational surface maps, Duke Math. J., 128 (2005), 331-368. | MR | Zbl
and ,6. Limit distribution of small points on algebraic tori, Duke Math. J., 89 (1997), 465-476 | MR | Zbl
,7. The Leech Lattice and Other Lattice, Thesis, Trinity College, Cambridge, 1984. | MR
,8. Groupes et algèbres de Lie, Chap. IV-VI, Hermann, 1968; Masson, 1981. | Zbl
,9. Dynamique des automorphismes des surfaces projectives complexes, C. R. Acad. Sci., Paris, Sér. I, Math., 328 (1999), 901-906 | MR | Zbl
,10. Dynamique des automorphismes des surfaces K3, Acta Math., 187 (2001), 1-57 | MR | Zbl
,11. Algebraic Geometry and Theta Functions, Colloquium Publications, vol. 10, Amer. Math. Soc., 1961. | JFM | MR
,12. Sphere Packings, Lattices and Groups. Springer, 1999. | MR | Zbl
and ,13. Point Sets in Projective Spaces and Theta Functions. Astérisque, vol. 165, 1988. | Numdam | MR | Zbl
and ,14. Coble rational surfaces, Amer. J. Math., 123 (2001), 79-114 | MR | Zbl
, ,15. Laminar currents and birational dynamics, Duke Math. J., 131 (2006), 219-247 | MR | Zbl
,16. Small Salem numbers, in Number Theory in Progress, vol. I, pp. 165-168, de Gruyter, 1999. | MR | Zbl
, , and ,17. Rational G-surfaces, Math. USSR Izv., 16 (1981), 103-134 | Zbl
,18. Principles of Algebraic Geometry, Wiley Interscience, 1978. | MR | Zbl
and ,19. On the entropy of holomorphic maps, Enseign. Math., 49 (2003), 217-235 | MR | Zbl
,20. Blowings-up of P2 and their blowings-down, Duke Math. J., 52 (1985), 129-148 | MR | Zbl
,21. Automorphisms of K3-like rational surfaces, in Algebraic Geometry, Bowdoin, 1985, Proc. Symp. Pure Math., vol. 48, pp. 17-28. Amer. Math. Soc., 1987. | MR | Zbl
,22. Rational surfaces with infinite automorphism group and no antipluricanonical curve, Proc. Amer. Math. Soc., 99 (1987), 409-414 | MR | Zbl
,23. Iterated blow-ups and moduli for rational surfaces, in Algebraic Geometry (Sundance, UT, 1986), Lect. Notes Math., vol. 1311, pp. 101-117, Springer, 1988. | MR | Zbl
,24. Moduli of Curves, Springer, 1998. | MR | Zbl
and ,25. Algebraic Geometry, Springer, 1977. | MR | Zbl
,26. Singularity confinement and chaos in discrete systems, Phys. Rev. Lett., 81 (1997), 325-328
, ,27. Symétries des surfaces rationnelles génériques, Math. Ann., 281 (1988), 255-261 | MR | Zbl
,28. Reflection Groups and Coxeter Groups, Cambridge University Press, 1990. | MR | Zbl
,29. Theorie der endlichen Gruppen von eindeutigen Transformationen in der Ebene, Mayer & Müller, 1895. | JFM
,30. Rational surfaces with an anticanonical cycle, Ann. Math., 114 (1981), 267-322 | MR | Zbl
,31. Rational surfaces over perfect fields, II, Math. USSR Sb., 1 (1967), 141-168 | Zbl
,32. Cubic Forms. Algebra, Geometry, Arithmetic, North-Holland Publishing Co., 1986. | MR | Zbl
,33. Pisot numbers from stars, in Number Theory in Progress, vol. I, pp. 309-319, de Gruyter, 1999. | MR | Zbl
, , and ,34. Coxeter groups, Salem numbers and the Hilbert metric, Publ. Math., Inst. Hautes Étud. Sci., 95 (2002), 151-183 | Numdam | MR
,35. Dynamics on K3 surfaces: Salem numbers and Siegel disks, J. Reine Angew. Math. 545 (2002), 201-233. | MR | Zbl
,36. On rational surfaces. I. Irreducible curves of arithmetic genus 0 or 1, Mem. Coll. Sci. Univ. Kyoto Ser. A Math., 32 (1960), 351-370 | MR | Zbl
,37. On rational surfaces. II, Mem. Coll. Sci. Univ. Kyoto Ser. A Math. 33 (1961), 271-293. | MR | Zbl
,38. Discrete reflection groups in Lobachevsky spaces and algebraic surfaces, in Proceedings of the International Congress of Mathematicians, pp. 654-671, Amer. Math. Soc., 1986. | MR | Zbl
,39. Irreducible Coxeter groups, Preprint, 2005. | MR
,40. A quadratic mapping with invariant cubic curve, Math. Proc. Camb. Philos. Soc., 89 (1981), 89-105 | MR | Zbl
, ,41. On Bilu's equidstribution theorem, Contemp. Math., 237 (1999), 159-166 | Zbl
,42. Algebraic Numbers and Fourier Analysis, Wadsworth, 1983. | MR | Zbl
,43. Rational points on K3 surfaces: A new canonical height, Invent. math., 105 (1991), 347-373 | MR | Zbl
,44. Algebraic entropy and the space of initial values for discrete dynamical systems. J. Phys. A, 34 (2001), 10533-10545. | MR | Zbl
,45. On the Kantor group of a set of points in a plane, Proc. London Math. Soc., 42 (1936), 18-51 | JFM
,46. Rational points and canonical heights on K3-surfaces in P 1×P 1×P 1, in Recent Developments in the Inverse Galois Problem, pp. 273-289, Amer. Math. Soc., 1995. | MR | Zbl
,47. Automorphisms of finite order on rational surfaces. With an appendix by I. Dolgachev, J. Algebra 238 (2001), 560-589. | MR | Zbl
,Cité par Sources :