Reducibility of 2-Dimensional Ultra-Differentiable Quasi-Periodic Systems with Small Parameters Under Brjuno-Rüssmann Condition

• Shoujun Xu ^[1] ; Hao Wu ^[2] ; Junxiang Xu ^[2]
  1. [1] Hefei University

     Hefei University

     China

     
  2. [2] Southeast University

     Southeast University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 1, 2025
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • In this article, we delve into whether a two-dimensional ultra-differentiable quasiperiodic system can be reduced. This system is characterized by a coefficient matrix that varies smoothly with a small parameter. We establish, under the adapted BrjunoRüssmann non-resonance condition concerning the basic frequencies and without imposing any non-degeneracy assumptions related to the small parameter, that the system can indeed be reduced through an ultra-differentiable quasi-periodic linear transformation for a substantial set of parameters, as perceived in the Lebesgue measure sense.

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