Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/2380
Type: Artigo de periódico
Title: On global linearization of planar involutions
Author: Pires, Benito
Teixeira, Marco Antonio
Abstract: Let phi: a"e(2) -> a"e(2) be an orientation-preserving C (1) involution such that phi(0) = 0. Let Spc(phi) = {Eigenvalues of D phi(p) | p a a"e(2)}. We prove that if Spc(phi) aS, a"e or Spc(phi) a (c) [1, 1 + epsilon) = a... for some epsilon > 0, then phi is globally C (1) conjugate to the linear involution D phi(0) via the conjugacy h = (I + D phi(0)phi)/2,where I: a"e(2) -> a"e(2) is the identity map. Similarly, we prove that if phi is an orientation-reversing C (1) involution such that phi(0) = 0 and Trace (D phi(0)D phi(p) > - 1 for all p a a"e(2), then phi is globally C (1) conjugate to the linear involution D phi(0) via the conjugacy h. Finally, we show that h may fail to be a global linearization of phi if the above conditions are not fulfilled.
Subject: planar involution
linearization
smooth conjugacy
fixed point
Editor: Springer
Rights: fechado
Identifier DOI: 10.1007/s00574-012-0030-2
Date Issue: 2012
Appears in Collections:IMECC - Artigos e Outros Documentos

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