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Smooth linearisation of planar periodic maps

Published online by Cambridge University Press:  21 May 2018

A. CIMA ,
A. GASULL ,
F. MAÑOSAS  and
R. ORTEGA
A. CIMA
Affiliation:
Departament de Matemàtiques, Edifici C Universitat Autònoma de Barcelona, Bellaterra (Barcelona), Spain. e-mails: cima@mat.uab.cat; gasull@mat.uab.cat; manyosas@mat.uab.cat
A. GASULL
Affiliation:
Departament de Matemàtiques, Edifici C Universitat Autònoma de Barcelona, Bellaterra (Barcelona), Spain. e-mails: cima@mat.uab.cat; gasull@mat.uab.cat; manyosas@mat.uab.cat
F. MAÑOSAS
Affiliation:
Departament de Matemàtiques, Edifici C Universitat Autònoma de Barcelona, Bellaterra (Barcelona), Spain. e-mails: cima@mat.uab.cat; gasull@mat.uab.cat; manyosas@mat.uab.cat
R. ORTEGA
Affiliation:
Departamento de Matemática Aplicada, Universidad de Granada, Granada, Spain. e-mail: rortega@ugr.es
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Abstract

The celebrated Kerékjártó theorem asserts that planar continuous periodic maps can be continuously linearised. We prove that for each k ∈ {1, 2,. . ., ∞}, ${\Mathcal {C}}$k-planar periodic maps can be ${\Mathcal {C}}$k-linearised.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 167 , Issue 2 , September 2019 , pp. 295 - 320
Copyright
Copyright © Cambridge Philosophical Society 2018 

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