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Divergence and convergence of conjugacies in non-Archimedean dynamics
Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics. (Mathematical modelling)ORCID iD: 0000-0002-7825-4428
2010 (English)In: Contemporary Mathematics, ISSN 0271-4132, E-ISSN 1098-3627, Vol. 508, p. 89-109Article in journal (Refereed) Published
Abstract [en]

We continue the study of the linearizability near an indifferent fixed point of a power series f, defined over a field of prime characteristic p. It is known since the work of Herman and Yoccoz in 1981 that Siegel’s linearization theorem is true also for non-Archimedean fields. However, they also showed that the condition in Siegel’s theorem is ‘usually’ not satisfied over fields of prime characteristic. Indeed, as proven by the author in a former paper, there exist power series f such that the associated conjugacy function diverges. We prove that if the degrees of the monomials of a power series f are divisible by p, then f is analytically linearizable. We find a lower (sometimes the best) bound of the size of the corresponding linearization disc. In the cases where we find the exact size of the linearization disc, we show, using the Weierstrass degree of the conjugacy, that f has an indifferent periodic point on the boundary. We also give a class of polynomials containing a monomial of degree prime to p, such that the conjugacy diverges.

Place, publisher, year, edition, pages
Providence, RI: Amer. Math. Soc. , 2010. Vol. 508, p. 89-109
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-7589OAI: oai:DiVA.org:lnu-7589DiVA, id: diva2:344780
Projects
Mathematical modelling, Linnaeus UniversityAvailable from: 2010-08-20 Created: 2010-08-20 Last updated: 2017-12-12Bibliographically approved

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Lindahl, Karl-Olof

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