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Generic parabolic points are isolated in positive characteristic
Linnaeus University, Faculty of Technology, Department of Mathematics. (Mathematical Modelling)ORCID iD: 0000-0002-7825-4428
Universidad Católica de Chile, Chile.
2016 (English)In: Nonlinearity, ISSN 0951-7715, E-ISSN 1361-6544, Vol. 29, no 5, 1596-1621 p.Article in journal (Refereed) Published
Abstract [en]

We study germs in one variable having a parabolic fixed point at the origin, over an ultrametric ground field of positive characteristic. It is conjectured that for such a germ the origin is isolated as a periodic point. Our main result is an affirmative solution of this conjecture in the case of a generic germ with a prescribed multiplier. The genericity condition is explicit: That the power series is minimally ramified, i.e., that the degree of the first nonlinear term of each of its iterates is as small as possible. Our main technical result is a computation of the first significant terms of a minimally ramified power series. From this we obtain a lower bound for the norm of nonzero periodic points, from which we deduce our main result. As a by-product we give a new and self-contained proof of a characterization of minimally ramified power series in terms of the iterative residue.

Place, publisher, year, edition, pages
Institute of Physics Publishing (IOPP), 2016. Vol. 29, no 5, 1596-1621 p.
National Category
Other Mathematics
Research subject
Mathematics, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-46164DOI: 10.1088/0951-7715/29/5/1596ISI: 000375008200006Scopus ID: 2-s2.0-84963815028OAI: oai:DiVA.org:lnu-46164DiVA: diva2:852303
Funder
The Royal Swedish Academy of Sciences
Available from: 2015-09-08 Created: 2015-09-08 Last updated: 2016-09-02Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
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  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
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  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
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  • Other locale
More languages
Output format
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  • text
  • asciidoc
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