A p -adic approach to local analytic dynamics: analytic conjugacy of analytic maps tangent to the identity

Adrian Jenkins[1]; Steven Spallone[2]

  • [1] Department of Mathematics, Kansas State University, Manhattan, KS, 66506
  • [2] Department of Mathematics, University of Oklahoma, Norman, OK, 73072

Annales de la faculté des sciences de Toulouse Mathématiques (2009)

  • Volume: 18, Issue: 3, page 611-634
  • ISSN: 0240-2963

Abstract

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In this note, we consider the question of local analytic equivalence of analytic functions which fix the origin and are tangent to the identity. All mappings and equivalences are considered in the non-archimedean context e.g. all norms can be considered p -adic norms. We show that any two mappings f and g which are formally equivalent are also analytically equivalent. We consider the related questions of roots and centralizers for analytic mappings. In this setting, anything which can be done formally can also be done analytically.

How to cite

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Jenkins, Adrian, and Spallone, Steven. "A $p$-adic approach to local analytic dynamics: analytic conjugacy of analytic maps tangent to the identity." Annales de la faculté des sciences de Toulouse Mathématiques 18.3 (2009): 611-634. <http://eudml.org/doc/10120>.

@article{Jenkins2009,
abstract = {In this note, we consider the question of local analytic equivalence of analytic functions which fix the origin and are tangent to the identity. All mappings and equivalences are considered in the non-archimedean context e.g. all norms can be considered $p$-adic norms. We show that any two mappings $f$ and $g$ which are formally equivalent are also analytically equivalent. We consider the related questions of roots and centralizers for analytic mappings. In this setting, anything which can be done formally can also be done analytically.},
affiliation = {Department of Mathematics, Kansas State University, Manhattan, KS, 66506; Department of Mathematics, University of Oklahoma, Norman, OK, 73072},
author = {Jenkins, Adrian, Spallone, Steven},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {analytic maps; non-archimedean fields},
language = {eng},
month = {7},
number = {3},
pages = {611-634},
publisher = {Université Paul Sabatier, Toulouse},
title = {A $p$-adic approach to local analytic dynamics: analytic conjugacy of analytic maps tangent to the identity},
url = {http://eudml.org/doc/10120},
volume = {18},
year = {2009},
}

TY - JOUR
AU - Jenkins, Adrian
AU - Spallone, Steven
TI - A $p$-adic approach to local analytic dynamics: analytic conjugacy of analytic maps tangent to the identity
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2009/7//
PB - Université Paul Sabatier, Toulouse
VL - 18
IS - 3
SP - 611
EP - 634
AB - In this note, we consider the question of local analytic equivalence of analytic functions which fix the origin and are tangent to the identity. All mappings and equivalences are considered in the non-archimedean context e.g. all norms can be considered $p$-adic norms. We show that any two mappings $f$ and $g$ which are formally equivalent are also analytically equivalent. We consider the related questions of roots and centralizers for analytic mappings. In this setting, anything which can be done formally can also be done analytically.
LA - eng
KW - analytic maps; non-archimedean fields
UR - http://eudml.org/doc/10120
ER -

References

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