On simultaneous linearization View Full Text


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Article Info

DATE

2019-03-28

AUTHORS

Alastair Fletcher, Douglas Macclure

ABSTRACT

Given a uniformly quasiregular mapping, there is typically no reason to assume any relationship between linearizers at different repelling periodic points. However, in the current paper we prove that in the case where the uqr map arises as a solution of a Schröder equation then, with some further natural assumptions, if L is a linearizer at one repelling periodic point, then L∘T is a linearizer at another repelling periodic point, where T is a translation. In this sense we say L simultaneously linearizes f. In the plane, an example would be that ez simultaneously linearizes z2. Our methods utilize generalized derivatives for quasiregular mappings, including a chain rule and inverse derivative formula which may be of independent interest. More... »

PAGES

1-29

References to SciGraph publications

  • 2016-06. On the infinitesimal space of UQR mappings in THE JOURNAL OF ANALYSIS
  • 1998. On the Asymptotic Behavior of Quasiconformal Mappings in Space in QUASICONFORMAL MAPPINGS AND ANALYSIS
  • 2015-06. On Quasiregular Linearizers in COMPUTATIONAL METHODS AND FUNCTION THEORY
  • 1993. Quasiregular Mappings in NONE
  • 2001. Lectures on Analysis on Metric Spaces in NONE
  • Journal

    TITLE

    Aequationes mathematicae

    ISSUE

    N/A

    VOLUME

    N/A

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00010-019-00643-y

    DOI

    http://dx.doi.org/10.1007/s00010-019-00643-y

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1113053639


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