Dynamics on blowups of the projective plane
Publications Mathématiques de l'IHÉS, Volume 105 (2007), p. 49-89
@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},
     publisher = {Springer},
     volume = {105},
     year = {2007},
     pages = {49-89},
     doi = {10.1007/s10240-007-0004-x},
     zbl = {pre05223501},
     mrnumber = {2354205},
     language = {en},
     url = {http://www.numdam.org/item/PMIHES_2007__105__49_0}
}
McMullen, Curtis T. Dynamics on blowups of the projective plane. Publications Mathématiques de l'IHÉS, Volume 105 (2007) pp. 49-89. doi : 10.1007/s10240-007-0004-x. http://www.numdam.org/item/PMIHES_2007__105__49_0/

1. M.F. Atiyah, R. Bott, A Lefschetz fixed point formula for elliptic complexes II, Ann. Math., 88 (1968), 451-491 | MR 232406 | Zbl 0167.21703

2. G. Bastien, M. Rogalski, 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 1070.39025

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 2280499

5. E. Bedford and J. Diller, Energy and invariant measures for birational surface maps, Duke Math. J., 128 (2005), 331-368. | MR 2140266 | Zbl 1076.37031

6. Y. Bilu, Limit distribution of small points on algebraic tori, Duke Math. J., 89 (1997), 465-476 | MR 1470340 | Zbl 0918.11035

7. R. E. Borcherds, The Leech Lattice and Other Lattice, Thesis, Trinity College, Cambridge, 1984. | MR 791880

8. N. Bourbaki, Groupes et algèbres de Lie, Chap. IV-VI, Hermann, 1968; Masson, 1981. | Zbl 0483.22001

9. S. Cantat, Dynamique des automorphismes des surfaces projectives complexes, C. R. Acad. Sci., Paris, Sér. I, Math., 328 (1999), 901-906 | MR 1689873 | Zbl 0943.37021

10. S. Cantat, Dynamique des automorphismes des surfaces K3, Acta Math., 187 (2001), 1-57 | MR 1864630 | Zbl 1045.37007

11. A. B. Coble, Algebraic Geometry and Theta Functions, Colloquium Publications, vol. 10, Amer. Math. Soc., 1961. | JFM 55.0808.02 | MR 123958

12. J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups. Springer, 1999. | MR 1662447 | Zbl 0915.52003

13. I. Dolgachev and D. Ortland, Point Sets in Projective Spaces and Theta Functions. Astérisque, vol. 165, 1988. | MR 1007155 | Zbl 0685.14029

14. I. Dolgachev, D.-Q. Zhang, Coble rational surfaces, Amer. J. Math., 123 (2001), 79-114 | MR 1827278 | Zbl 1056.14054

15. R. Dujardin, Laminar currents and birational dynamics, Duke Math. J., 131 (2006), 219-247 | MR 2219241 | Zbl 1099.37037

16. V. Flammang, M. Grandcolas, and G. Rhin, Small Salem numbers, in Number Theory in Progress, vol. I, pp. 165-168, de Gruyter, 1999. | MR 1689505 | Zbl 0935.11038

17. M. Gizatullin, Rational G-surfaces, Math. USSR Izv., 16 (1981), 103-134 | Zbl 0465.14017

18. P. Griffiths and J. Harris, Principles of Algebraic Geometry, Wiley Interscience, 1978. | MR 507725 | Zbl 0408.14001

19. M. Gromov, On the entropy of holomorphic maps, Enseign. Math., 49 (2003), 217-235 | MR 2026895 | Zbl 1080.37051

20. B. Harbourne, Blowings-up of P2 and their blowings-down, Duke Math. J., 52 (1985), 129-148 | MR 791295 | Zbl 0577.14025

21. B. Harbourne, 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 927971 | Zbl 0651.14023

22. B. Harbourne, Rational surfaces with infinite automorphism group and no antipluricanonical curve, Proc. Amer. Math. Soc., 99 (1987), 409-414 | MR 875372 | Zbl 0643.14019

23. B. Harbourne, 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 951643 | Zbl 0661.14030

24. J. Harris and I. Morrison, Moduli of Curves, Springer, 1998. | MR 1631825 | Zbl 0913.14005

25. R. Hartshorne, Algebraic Geometry, Springer, 1977. | MR 463157 | Zbl 0367.14001

26. J. Hietarinta, C. Viallet, Singularity confinement and chaos in discrete systems, Phys. Rev. Lett., 81 (1997), 325-328

27. A. Hirschowitz, Symétries des surfaces rationnelles génériques, Math. Ann., 281 (1988), 255-261 | MR 949832 | Zbl 0662.14024

28. J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge University Press, 1990. | MR 1066460 | Zbl 0768.20016

29. S. Kantor, Theorie der endlichen Gruppen von eindeutigen Transformationen in der Ebene, Mayer & Müller, 1895. | JFM 26.0770.03

30. E. Looijenga, Rational surfaces with an anticanonical cycle, Ann. Math., 114 (1981), 267-322 | MR 632841 | Zbl 0509.14035

31. Y. Manin, Rational surfaces over perfect fields, II, Math. USSR Sb., 1 (1967), 141-168 | Zbl 0182.23701

32. Y. Manin, Cubic Forms. Algebra, Geometry, Arithmetic, North-Holland Publishing Co., 1986. | MR 833513 | Zbl 0277.14014

33. J. F. Mckee, P. Rowlinson, and C. J. Smyth, Pisot numbers from stars, in Number Theory in Progress, vol. I, pp. 309-319, de Gruyter, 1999. | MR 1689512 | Zbl 0931.11041

34. C. Mcmullen, Coxeter groups, Salem numbers and the Hilbert metric, Publ. Math., Inst. Hautes Étud. Sci., 95 (2002), 151-183 | Numdam | MR 1953192 | Zbl pre01874454

35. C. Mcmullen, Dynamics on K3 surfaces: Salem numbers and Siegel disks, J. Reine Angew. Math. 545 (2002), 201-233. | MR 1896103 | Zbl 1054.37026

36. M. Nagata, 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 126443 | Zbl 0100.16703

37. M. Nagata, On rational surfaces. II, Mem. Coll. Sci. Univ. Kyoto Ser. A Math. 33 (1961), 271-293. | MR 126444 | Zbl 0100.16801

38. V. V. Nikulin, 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 934268 | Zbl 0671.22006

39. L. Paris, Irreducible Coxeter groups, Preprint, 2005. | MR 2333366 | Zbl pre05172231

40. R. Penrose, C.A.B. Smith, A quadratic mapping with invariant cubic curve, Math. Proc. Camb. Philos. Soc., 89 (1981), 89-105 | MR 591975 | Zbl 0453.14005

41. R. Rumely, On Bilu's equidstribution theorem, Contemp. Math., 237 (1999), 159-166 | Zbl 1029.11030

42. R. Salem, Algebraic Numbers and Fourier Analysis, Wadsworth, 1983. | MR 732447 | Zbl 0505.00033

43. J. Silverman, Rational points on K3 surfaces: A new canonical height, Invent. math., 105 (1991), 347-373 | MR 1115546 | Zbl 0754.14023

44. T. Takenawa, Algebraic entropy and the space of initial values for discrete dynamical systems. J. Phys. A, 34 (2001), 10533-10545. | MR 1877473 | Zbl 0999.37028

45. P. Du Val, On the Kantor group of a set of points in a plane, Proc. London Math. Soc., 42 (1936), 18-51 | JFM 62.0751.02

46. L. Wang, 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 1352278 | Zbl 0849.14010

47. D.-Q. Zhang, Automorphisms of finite order on rational surfaces. With an appendix by I. Dolgachev, J. Algebra 238 (2001), 560-589. | MR 1823774 | Zbl 1057.14053