Equivariant Nonautonomous Normal Forms

• Barreira, Luis ^[1] ; Valls, Claudia ^[1]
  1. [1] Universidade de Lisboa

     Universidade de Lisboa

     Socorro, Portugal

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 20, Nº 3, 2021
• Idioma: inglés
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• Resumen

  • For a nonautonomous dynamics with discrete time, we show that if the dynamics is equivariant (respectively, reversible), then any normal form as well as the coordinate change bringing the dynamics to this normal form have equivariance (respectively, reversibility) properties. The resonances of the linear part of the dynamics are expressed in terms of the nonuniform spectrum, that in its turn is defined in terms of the notion of a tempered exponential dichotomy.