Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/90161
Type: Artigo de periódico
Title: On Global Linearization Of Planar Involutions
Author: Pires B.
Teixeira M.A.
Abstract: Let φ: ℝ 2 → ℝ 2 be an orientation-preserving C 1 involution such that φ(0) = 0. Let Spc(φ) = {Eigenvalues of Dφ(p) {pipe} p ∈ ℝ 2}. We prove that if Spc(φ) ⊂ ℝ or Spc(φ) ∩ [1, 1 + ε) = ∅ for some ε > 0, then φ is globally C 1 conjugate to the linear involution Dφ(0) via the conjugacy h = (I + Dφ(0)φ)/2,where I: ℝ 2 → ℝ 2 is the identity map. Similarly, we prove that if φ is an orientation-reversing C 1 involution such that φ(0) = 0 and Trace (Dφ(0)Dφ(p) > - 1 for all p ∈ ℝ 2, then φ is globally C 1 conjugate to the linear involution Dφ(0) via the conjugacy h. Finally, we show that h may fail to be a global linearization of φ if the above conditions are not fulfilled. © 2012 Sociedade Brasileira de Matemática.
Editor: 
Rights: fechado
Identifier DOI: 10.1007/s00574-012-0030-2
Address: http://www.scopus.com/inward/record.url?eid=2-s2.0-84869124618&partnerID=40&md5=72e4f1a3d047a60898551ea098d3233d
Date Issue: 2012
Appears in Collections:Unicamp - Artigos e Outros Documentos

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