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Divergence and convergence of conjugacies in non-Archimedean dynamicsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2010 (English)In: Contemporary Mathematics, ISSN 0271-4132, E-ISSN 1098-3627, Vol. 508, p. 89-109Article in journal (Refereed) Published
##### Abstract [en]

##### 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
#####

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##### Projects

Mathematical modelling, Linnaeus UniversityAvailable from: 2010-08-20 Created: 2010-08-20 Last updated: 2017-12-12Bibliographically approved

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.

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