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Optimal cycles in ultrametric dynamics and minimally ramified power series
Linnaeus University, Faculty of Technology, Department of Mathematics. (Mathematical Modelling)ORCID iD: 0000-0002-7825-4428
Pontífica Univerisdád Católica de Santiago de Chile, Chile.
2016 (English)In: Compositio Mathematica, ISSN 0010-437X, E-ISSN 1570-5846, Vol. 152, no 01, p. 187-222Article in journal (Refereed) Published
Abstract [en]

We study ultrametric germs in one variable having an irrationally indifferent fixed point at the origin with a prescribed multiplier. We show that for many values of the multiplier, the cycles in the unit disk of the corresponding monic quadratic polynomial are "optimal" in the following sense: They minimize the distance to the origin among cycles of the same minimal period of normalized germs having an irrationally indifferent fixed point at the origin with the same multiplier. We also give examples of multipliers for which the corresponding quadratic polynomial does not have optimal cycles. In those cases we exhibit a higher degree polynomial such that all of its cycles are optimal. The proof of these results reveals a connection between the geometric location of periodic points of ultrametric power series and the lower ramification numbers of wildly ramified field automorphisms. We also give an extension of Sen's theorem on wildly ramified field automorphisms that is of independent interest.

Place, publisher, year, edition, pages
London: London Mathematical Society, 2016. Vol. 152, no 01, p. 187-222
National Category
Mathematics
Research subject
Mathematics, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-31546DOI: 10.1112/S0010437X15007575ISI: 000369432300006Scopus ID: 2-s2.0-84955741084OAI: oai:DiVA.org:lnu-31546DiVA, id: diva2:689589
Note

Finansierad av SVeFUM Stiftelsen för svensk forskning och utbildning i Matematik, och MECESUP II, FONDECYT (Chile)

Available from: 2014-01-21 Created: 2014-01-21 Last updated: 2017-12-06Bibliographically approved

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Lindahl, Karl-Olof

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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf