Eigenvaluations

 Access to full text

 Full (PDF)

1. [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. Zbl0272.12102
2. [2] Bedford E., Jonsson M., Dynamics of regular polynomial endomorphisms of $C^k$, Amer. J. Math.122 (2000) 153-212. Zbl0941.37027MR1737260
3. [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. Zbl1074.14505MR1888423
4. [4] Carleson L., Gamelin T.W., Complex Dynamics, Universitext: Tracts in Mathematics, Springer-Verlag, New York, 1993. Zbl0782.30022MR1230383
5. [5] Cutkosky S.D., Monomialization of Morphisms from 3-Folds to Surfaces, Lecture Notes in Mathematics, vol. 1786, Springer-Verlag, Berlin, 2002. Zbl1057.14009MR1927974
6. [6] Demailly J.-P., Complex analytic and algebraic geometry, Book available at the website, http://www-fourier.ujf-grenoble.fr/~demailly/books.html. 
7. [7] Diller J., Favre C., Dynamics of bimeromorphic maps of surfaces, Amer. J. Math.123 (2001) 1135-1169. Zbl1112.37308MR1867314
8. [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. Zbl1079.37040MR2195140
9. [9] Favre C., Classification of 2-dimensional contracting rigid germs and Kato surfaces. I, J. Math. Pures Appl. (9)79 (5) (2000) 475-514. Zbl0983.32023MR1759437
10. [10] Favre C., Guedj V., Dynamique des applications rationnelles des espaces multiprojectifs, Indiana Univ. Math. J.50 (2) (2001) 881-934. Zbl1046.37026MR1871393
11. [11] Favre C., Jonsson M., Brolin's theorem for curves in two complex dimensions, Ann. Inst. Fourier53 (2003) 1461-1501. Zbl1113.32005MR2032940
12. [12] Favre C., Jonsson M., The Valuative Tree, Lecture Notes in Mathematics, vol. 1853, Springer-Verlag, Berlin, 2004. Zbl1064.14024MR2097722
13. [13] Favre C., Jonsson M., Valuative analysis of planar plurisubharmonic functions, Invent. Math.162 (2) (2005) 271-311. Zbl1089.32032MR2199007
14. [14] Favre C., Jonsson M., Valuations and multiplier ideals, J. Amer. Math. Soc.18 (2005) 655-684. Zbl1075.14001MR2138140
15. [15] Fujimoto M., Suzuki M., Construction of affine plane curves with one place at infinity, Osaka J. Math.39 (2002) 1005-1027. Zbl1053.14069MR1951527
16. [16] Griffiths P., Harris J., Principles of Algebraic Geometry, Wiley Classics Library, John Wiley & Sons Inc., New York, 1994. Zbl0836.14001MR1288523
17. [17] Hubbard J.H., Papadopol P., Superattractive fixed points in $C^n$, Indiana Univ. Math. J.43 (1) (1994) 321-365. Zbl0858.32023MR1275463
18. [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. Zbl1133.37018
19. [19] MacLane S., A construction for prime ideals as absolute values of an algebraic field, Duke Math. J.2 (1936) 363-395. Zbl62.1106.02MR1545943JFM62.0096.02
20. [20] Moh T.T., On analytic irreducibility at ∞ of a pencil of curves, Proc. Amer. Math. Soc.44 (1974) 22-24. Zbl0309.14011
21. [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. Zbl0943.11001MR2404578
22. [22] Morgan J.M., Shalen P.B., Valuations, trees, and degenerations of hyperbolic structures, I, Ann. Math.120 (1984) 401-476. Zbl0583.57005MR769158
23. [23] Nguyen V.-A., Algebraic degrees for iterates of meromorphic self-maps of $P^k$, Publ. Mat.50 (2006) 457-473. Zbl1112.37035MR2273670
24. [24] Paulin F., Actions de groupes sur les arbres, Astérisque241 (1997), Exp. No. 808, 3, 97–137. Zbl0984.20015
25. [25] Rivera-Letelier J., Espace hyperbolique p-adique et dynamique des fonctions rationnelles, Compositio Math.138 (2) (2003) 199-231. Zbl1041.37021MR2018827
26. [26] Rivera-Letelier J., Sur la structure des ensembles de Fatou p-adiques, Preprint available at, http://www.math.sunysb.edu/~rivera. 
27. [27] Russakovskii A., Shiffman B., Value distribution for sequences of rational mappings and complex dynamics, Indiana Univ. Math. J.46 (3) (1997) 897-932. Zbl0901.58023MR1488341
28. [28] Shub M., Global Stability of Dynamical Systems, Springer-Verlag, New York–Heidelberg–Berlin, 1987. Zbl0606.58003
29. [29] Sibony N., Dynamique des applications rationnelles de $P^k$, Panor. Synthèses8 (1999) 97-185. Zbl1020.37026MR1760844
30. [30] Suzuki M., Propriétés topologiques des polynômes de deux variables complexes, et automorphismes algébriques de l’espace $C^2$, J. Math. Soc. Japan26 (1974) 241-257. Zbl0276.14001MR338423
31. [31] Vigny G., Dynamics semi-conjugated to a subshift for some polynomial mappings in $C^2$, Publ. Mat.51 (2007) 201-222. Zbl1125.37035MR2307152
32. [32] Zariski O., Samuel P., Commutative Algebra, vol. 2, Graduate Texts in Mathematics, vol. 29, Springer-Verlag, New York–Heidelberg–Berlin, 1975. Zbl0313.13001

1. Matteo Ruggiero, Contracting rigid germs in higher dimensions
2. Tien-Cuong Dinh, Nessim Sibony, Equidistribution towards the Green current for holomorphic maps