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Classification of one-dimensional superattracting germs in positive characteristic

Published online by Cambridge University Press:  05 August 2014

MATTEO RUGGIERO
MATTEO RUGGIERO*
Affiliation:
Fondation Mathématique Jacques Hadamard (FMJH), Centre de Mathématiques Laurent Schwartz, École Polytechnique, 91128 Palaiseau Cedex, France email [email protected]
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Abstract

We give a classification of superattracting germs in dimension $1$ over a complete normed algebraically closed field $\mathbb{K}$ of positive characteristic up to conjugacy. In particular, we show that formal and analytic classifications coincide for these germs. We also give a higher-dimensional version of some of these results.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 7 , October 2015 , pp. 2242 - 2268
Copyright
© Cambridge University Press, 2014 

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References

Berteloot, F.. Méthodes de changement d’échelles en analyse complexe. Ann. Fac. Sci. Toulouse Math. (6) 15(3) (2006), 427–483.CrossRefGoogle Scholar
Böttcher, L. E.. The principal laws of convergence of iterates and their application to analysis (Russian). Izv. Kazan. Fiz.-Mat. Obshch. 14 (1904), 155–234.Google Scholar
Dloussky, G.. Structure des surfaces de Kato. Mém. Soc. Math. France (N.S.) 14 (1984), ii+120.Google Scholar
Dloussky, G. and Oeljeklaus, K.. Vector fields and foliations on compact surfaces of class VII0. Ann. Inst. Fourier (Grenoble) 49(5) (1999), 1503–1545.CrossRefGoogle Scholar
Dloussky, G., Oeljeklaus, K. and Toma, M.. Surfaces de la classe VII0 admettant un champ de vecteurs. II. Comment. Math. Helv. 76(4) (2001), 640–664.CrossRefGoogle Scholar
Favre, C.. Classification of 2-dimensional contracting rigid germs and Kato surfaces. I. J. Math. Pures Appl. (9) 79(5) (2000), 475–514.CrossRefGoogle Scholar
Favre, C. and Jonsson, M.. Eigenvaluations. Ann. Sci. École Norm. Sup. (4) 40(2) (2007), 309–349.CrossRefGoogle Scholar
Friedland, S. and Milnor, J.. Dynamical properties of plane polynomial automorphisms. Ergod. Th. & Dynam. Sys. 9(1) (1989), 67–99.CrossRefGoogle Scholar
Hubbard, J. H. and Oberste-Vorth, R. W.. Hénon mappings in the complex domain. I. The global topology of dynamical space. Inst. Hautes Études Sci. Publ. Math. 79 (1994), 5–46.CrossRefGoogle Scholar
Herman, M. and Yoccoz, J.-C.. Generalizations of some theorems of small divisors to non-Archimedean fields. Geometric Dynamics (Rio de Janeiro, 1981) (Lecture Notes in Mathematics, 1007). Springer, Berlin, 1983, pp. 408–447.CrossRefGoogle Scholar
Ilyashenko, Y. and Yakovenko, S.. Lectures on Analytic Differential Equations (Graduate Studies in Mathematics, 86). American Mathematical Society, Providence, RI, 2008.Google Scholar
Lindahl, K.-O.. On Siegel’s linearization theorem for fields of prime characteristic. Nonlinearity 17(3) (2004), 745–763.CrossRefGoogle Scholar
Nakamura, I.. On surfaces of class VII0 with curves. Invent. Math. 78(3) (1984), 393–443.CrossRefGoogle Scholar
Rosay, J.-P. and Rudin, W.. Holomorphic maps from Cn to Cn. Trans. Amer. Math. Soc. 310(1) (1988), 47–86.Google Scholar
Ruggiero, M.. Contracting rigid germs in higher dimensions. Ann. Inst. Fourier (Grenoble) 63(5) (2013), 1913–1950.CrossRefGoogle Scholar
Ruggiero, M.. Rigidification of holomorphic germs with noninvertible differential. Michigan Math. J. 61(1) (2012), 161–185.CrossRefGoogle Scholar
Spencer, M. G.. Moduli spaces of power series in finite characteristic. PhD Thesis, Brown University, Providence, 2011.Google Scholar
Sternberg, S.. Local contractions and a theorem of Poincaré. Amer. J. Math. 79 (1957), 809–824.CrossRefGoogle Scholar
Toma, M. On the Kähler rank of compact complex surfaces. Bull. Soc. Math. France 136(2) (2008), 243–260.CrossRefGoogle Scholar