Regularization of Brouwer Translation Theorem

• Armengol Gasull ^[1] ; Jorge Groisman ^[2] ; Francesc Mañosas ^[1]
  1. [1] Universitat Autònoma de Barcelona

     Universitat Autònoma de Barcelona

     Barcelona, España

     
  2. [2] Universidad de la República

     Universidad de la República

     Uruguay

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 4, 2022
• Idioma: inglés
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• Resumen

  • The celebrated Brouwer translation theorem asserts that for a preserving orientation fixed point free homeomorphism of the plane, each point belongs to an invariant region where the dynamics is continuously conjugate to a translation. In this work we prove that if we start with a Cm, m ∈ N ∪ {∞}, diffeomorphism then the referred conjugacy has the same kind of regularity.