A p-adic approach to local analytic dynamics: analytic conjugacy of analytic maps tangent to the identity
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 18 (2009) no. 3, p. 611-634

In this note, we consider the question of local analytic equivalence of analytic functions which fix the origin and are tangent to the identity. All mappings and equivalences are considered in the non-archimedean context e.g. all norms can be considered p-adic norms. We show that any two mappings f and g which are formally equivalent are also analytically equivalent. We consider the related questions of roots and centralizers for analytic mappings. In this setting, anything which can be done formally can also be done analytically.

Nous considérons la question d’équivalence locale de fonctions analytiques qui fixent l’origine et sont tangentes à l’identité. Toutes les fonctions et équivalences sont dans le contexte nonarchimédien, c’est-à-dire que nous pouvons considérer les normes comme étant des normes p-adiques. Nous démontrons que deux fonctions f et g formellement équivalentes sont aussi équivalentes analytiquement. Nous considérons la question des racines et centraliseurs pour les fonctions analytiques. Dans ce contexte, tout ce qui peut être prouvé formellement peut aussi être prouvé analytiquement.

@article{AFST_2009_6_18_3_611_0,
     author = {Jenkins, Adrian and Spallone, Steven},
     title = {A $p$-adic approach to local analytic dynamics: analytic conjugacy of analytic maps tangent to the identity},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 18},
     number = {3},
     year = {2009},
     pages = {611-634},
     doi = {10.5802/afst.1217},
     mrnumber = {2582444},
     zbl = {1185.37210},
     language = {en},
     url = {http://www.numdam.org/item/AFST_2009_6_18_3_611_0}
}
Jenkins, Adrian; Spallone, Steven. A $p$-adic approach to local analytic dynamics: analytic conjugacy of analytic maps tangent to the identity. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 18 (2009) no. 3, pp. 611-634. doi : 10.5802/afst.1217. http://www.numdam.org/item/AFST_2009_6_18_3_611_0/

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