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References
Y. Amice, Les nombres p-adiques, Presses Universitaires de France, Paris, 1975.
V.I. Arnold, Small denominators I, Mappings of circumference onto itself, Amer. Math. Soc. Transl. Ser. 2, 46 pp. 213–284.
M.R. Herman, Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations, Publ. I.H.E.S. 49 pp. 5–233.
E. Lutz, Sur les approximations diophantiennes linéaires p-adiques, Hermann, Paris, 1955.
K. Mahler, P-adic numbers and their functions, Camb. Univ. Press, Cambridge, second edition, 1981.
K. Meyer, The implicit function theorem and analytic differential equations, Springer Lect. Notes in Math. 468, Proc. Symp. on Dynamical Systems at Warwick (1974).
A.C.M. Van Rooij, Non archimedean function analysis, Marcel Dekker, New York, 1978.
H. Rűssmann, Kleine Nenner II: Bemerkungen zur Newton'schen Methode. Nachr. Akad. Wiss. Gőttingen Math. Phys. K1. (1972) pp. 1–20.
W.H. Schikhof, Non archimedean calculus, Lecture notes, Nijmegean, Katholieke Univ., 1978.
J.P. Serre, Lie algebras and Lie groups, Benjamin, New York, 1965.
Y. Sibuya & S. Sperber, Convergence of power series of p-adic non linear differential equations, preprint Univ. Minnesota (1978).
C.L. Siegel, Iteration of analytic functions, Ann. Math. 43 (1942), pp. 607–612.
C.L. Siegel, Űber die Normalform analytischer Differentialgleichungen in der Nähe einer Gleichawichtslösung, Nachr. Akad. Wiss. Gőttingen, Math. Phys. K. (1952), pp. 21–30.
C.S. Weisman, On p-adic differentiability, J. Number th. 9 (1977), pp. 79–86.
E. Zehnder, A simple proof of a generalization of a theorem by C.L. Siegel, Lec. Notes in Math. 597, Springer-Verlag, Berlin, (1977), pp. 855–866.
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© 1983 Springer-Verlag
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Herman, M., Yoccoz, J.C. (1983). Generalizations of some theorems of small divisors to non archimedean fields. In: Palis, J. (eds) Geometric Dynamics. Lecture Notes in Mathematics, vol 1007. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0061427
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DOI: https://doi.org/10.1007/BFb0061427
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