A New KAM Iteration with Nearly Infinitely Small Steps in Reversible Systems of Polynomial Character

Zhang, Dongfeng ^[1] ; Xu, Junxiang ^[1] ; Wang, Xiaocai ^[2]
1. [1] Southeast University
  
  Southeast University
  
  China
2. [2] Huaiyin Institute of Technology
  
  Huaiyin Institute of Technology
  
  China
Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 17, Nº 1, 2018, págs. 271-289
Idioma: inglés
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Resumen
- In this paper we prove the persistence of invariant tori of analytic reversible systems under Brjuno–Rüssmann’s non-resonant condition by an improved KAM iteration, but the frequency may undergo some drift. Furthermore, if the frequency mapping has nonzero Brouwer’s topological degree, then the invariant torus with prescribed frequency can persist. In the proof we propose a new method of KAM iteration for reversible systems, containing an artificial parameter q,0 q 1, which makes the steps of KAM iteration infinitely small in the speed of the function qnϵ rather than super exponential function ϵλn,1 λ 2.