Eigenvaluations

Favre, Charles; Jonsson, Mattias

doi:10.1016/j.ansens.2007.01.002

Eigenvaluations

Favre, Charles ; Jonsson, Mattias ¹

¹ University of Michigan, Department of Mathematics, Ann Arbor MI 48109-1109 (USA)

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 40 (2007) no. 2, pp. 309-349.

MR Zbl | 5 citations dans Numdam

DOI : 10.1016/j.ansens.2007.01.002

Affiliations des auteurs :

Favre, Charles ; Jonsson, Mattias ¹

¹ University of Michigan, Department of Mathematics, Ann Arbor MI 48109-1109 (USA)

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Favre, Charles; Jonsson, Mattias. Eigenvaluations. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 40 (2007) no. 2, pp. 309-349. doi : 10.1016/j.ansens.2007.01.002. http://www.numdam.org/articles/10.1016/j.ansens.2007.01.002/

Bibliographie
Cité par

[1] Abhyankar S.S., Moh T.T., Newton-Puiseux expansion and generalized Tschirnhausen transformation. I, J. reine angew. Math. 260 (1973) 47-83, Newton-Puiseux expansion and generalized Tschirnhausen transformation. II, J. reine angew. Math. 261 (1973) 29-53. | EuDML | Zbl

[2] Bedford E., Jonsson M., Dynamics of regular polynomial endomorphisms of $C^{k}$ , Amer. J. Math. 122 (2000) 153-212. | MR | Zbl

[3] Campillo A., Piltant O., Reguera-López A.J., Cones of curves and of line bundles on surfaces associated with curves having one place at infinity, Proc. London Math. Soc. (3) 84 (3) (2002) 559-580. | MR | Zbl

[4] Carleson L., Gamelin T.W., Complex Dynamics, Universitext: Tracts in Mathematics, Springer-Verlag, New York, 1993. | MR | Zbl

[5] Cutkosky S.D., Monomialization of Morphisms from 3-Folds to Surfaces, Lecture Notes in Mathematics, vol. 1786, Springer-Verlag, Berlin, 2002. | MR | Zbl

[6] Demailly J.-P., Complex analytic and algebraic geometry, Book available at the website, http://www-fourier.ujf-grenoble.fr/~demailly/books.html.

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

[8] Dinh T.C., Dujardin R., Sibony N., On the dynamics near infinity of some polynomial mappings of $C^{2}$ , Math. Ann. 333 (4) (2005) 703-739. | MR | Zbl

[9] Favre C., Classification of 2-dimensional contracting rigid germs and Kato surfaces. I, J. Math. Pures Appl. (9) 79 (5) (2000) 475-514. | MR | Zbl

[10] Favre C., Guedj V., Dynamique des applications rationnelles des espaces multiprojectifs, Indiana Univ. Math. J. 50 (2) (2001) 881-934. | MR | Zbl

[11] Favre C., Jonsson M., Brolin's theorem for curves in two complex dimensions, Ann. Inst. Fourier 53 (2003) 1461-1501. | EuDML | Numdam | MR | Zbl

[12] Favre C., Jonsson M., The Valuative Tree, Lecture Notes in Mathematics, vol. 1853, Springer-Verlag, Berlin, 2004. | MR | Zbl

[13] Favre C., Jonsson M., Valuative analysis of planar plurisubharmonic functions, Invent. Math. 162 (2) (2005) 271-311. | MR | Zbl

[14] Favre C., Jonsson M., Valuations and multiplier ideals, J. Amer. Math. Soc. 18 (2005) 655-684. | MR | Zbl

[15] Fujimoto M., Suzuki M., Construction of affine plane curves with one place at infinity, Osaka J. Math. 39 (2002) 1005-1027. | MR | Zbl

[16] Griffiths P., Harris J., Principles of Algebraic Geometry, Wiley Classics Library, John Wiley & Sons Inc., New York, 1994. | MR | Zbl

[17] Hubbard J.H., Papadopol P., Superattractive fixed points in $C^{n}$ , Indiana Univ. Math. J. 43 (1) (1994) 321-365. | MR | Zbl

[18] Hubbard J.H., Papadopol P., Newton's method applied to two quadratic equations in $C^{2}$ viewed as a global dynamical system, Mem. Amer. Math. Soc., in press. | Zbl

[19] Maclane S., A construction for prime ideals as absolute values of an algebraic field, Duke Math. J. 2 (1936) 363-395. | JFM | MR

[20] Moh T.T., On analytic irreducibility at ∞ of a pencil of curves, Proc. Amer. Math. Soc. 44 (1974) 22-24. | Zbl

[21] Mollin R.A., Fundamental Number Theory with Applications, CRC Press Series on Discrete Mathematics and its Applications, Chapman & Hall/CRC, Boca Raton, FL, 1997. | MR | Zbl

[22] Morgan J.M., Shalen P.B., Valuations, trees, and degenerations of hyperbolic structures, I, Ann. Math. 120 (1984) 401-476. | MR | Zbl

[23] Nguyen V.-A., Algebraic degrees for iterates of meromorphic self-maps of $P^{k}$ , Publ. Mat. 50 (2006) 457-473. | EuDML | MR | Zbl

[24] Paulin F., Actions de groupes sur les arbres, Astérisque 241 (1997), Exp. No. 808, 3, 97-137. | EuDML | Numdam | Zbl

[25] Rivera-Letelier J., Espace hyperbolique p-adique et dynamique des fonctions rationnelles, Compositio Math. 138 (2) (2003) 199-231. | MR | Zbl

[26] Rivera-Letelier J., Sur la structure des ensembles de Fatou p-adiques, Preprint available at, http://www.math.sunysb.edu/~rivera.

[27] 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

[28] Shub M., Global Stability of Dynamical Systems, Springer-Verlag, New York-Heidelberg-Berlin, 1987. | Zbl

[29] Sibony N., Dynamique des applications rationnelles de $P^{k}$ , Panor. Synthèses 8 (1999) 97-185. | MR | Zbl

[30] Suzuki M., Propriétés topologiques des polynômes de deux variables complexes, et automorphismes algébriques de l’espace $C^{2}$ , J. Math. Soc. Japan 26 (1974) 241-257. | MR | Zbl

[31] Vigny G., Dynamics semi-conjugated to a subshift for some polynomial mappings in $C^{2}$ , Publ. Mat. 51 (2007) 201-222. | EuDML | MR | Zbl

[32] Zariski O., Samuel P., Commutative Algebra, vol. 2, Graduate Texts in Mathematics, vol. 29, Springer-Verlag, New York-Heidelberg-Berlin, 1975.

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