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

Xuemei Li; Zaijiu Shang

doi:10.3934/dcds.2019171

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2019, Volume 39, Issue 7: 4225-4257. Doi: 10.3934/dcds.2019171

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

Xuemei Li^1, , and
Zaijiu Shang^2,

1.
Key Laboratory of High Performance Computing and Stochastic Information Processing, Department of Mathematics, Hunan Normal University, Changsha, Hunan 410081, China
2.
HLM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China

* Corresponding author: Xuemei Li
* Corresponding author: Xuemei Li

Received: October 31, 2018

Published: April 2019

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.

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

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