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On the existence of invariant tori in non-conservative dynamical systems with degeneracy and finite differentiability

  • * Corresponding author: Xuemei Li

    * Corresponding author: Xuemei Li 

This work is supported by the NNSF (11371132, 11671392) of China

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  • In this paper, we establish a KAM-theorem about the existenceof invariant tori in non-conservative dynamical systems with finitely differentiable vector fields and multiple degeneracies under the assumption that theintegrable part is finitely differentiable with respect to parameters, instead ofthe usual assumption of analyticity. We prove these results by constructingapproximation and inverse approximation lemmas in which all functions arefinitely differentiable in parameters.

    Mathematics Subject Classification: Primary: 37J40, 37K55; Secondary: 34A34, 34C15.


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