Linearization in ultrametric dynamics in fields of characteristic zero - equal characteristic case

Details Linearization in ultrametric dynamics in fields of characteristic zero - equal characteristic case Linearization in ultrametric dynamics in fields of characteristic zero - equal characteristic case

2011-11-08

arxiv.org/abs/1111.1993v1

p-Adic Numbers, Ultrametric Analysis and Applications, Vol. 1, No 4, pp. 307-316, 2009

Mathematics

Dynamical Systems

Scientific paper

10.1134/S2070046609040049

Let $K$ be a complete ultrametric field of charactersitic zero whose corresponding residue field $\Bbbk$ is also of charactersitic zero. We give lower and upper bounds for the size of linearization disks for power series over $K$ near an indifferent fixed point. These estimates are maximal in the sense that there exist exemples where these estimates give the exact size of the corresponding linearization disc. Similar estimates in the remaning cases, i.e. the cases in which $K$ is either a $p$-adic field or a field of prime characteristic, were obtained in various papers on the $p$-adic case (Ben-Menahem:1988,Thiran/EtAL:1989,Pettigrew/Roberts/Vivaldi:2001,Khrennikov:2001) later generalized in (Lindahl:2009 arXiv:0910.3312), and in (Lindahl:2004 http://iopscience.iop.org/0951-7715/17/3/001/,Lindahl:2010Contemp. Math) concerning the prime characteristic case.

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