Existence of invariant curves for area-preserving mappings under weaker non-degeneracy conditions

doi:10.1007/s11464-020-0838-9

Front. Math. China

2020, Vol. 15

Issue (3) : 571-591 https://doi.org/10.1007/s11464-020-0838-9

RESEARCH ARTICLE

Existence of invariant curves for area-preserving mappings under weaker non-degeneracy conditions

Kun WANG, Junxiang XU(

)

School of Mathematics, Southeast University, Nanjing 211189, China

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Abstract

We consider a class of analytic area-preserving mappings C^m-smoothly depending on a parameter. Without imposing on any non-degeneracy assumption, we prove a formal KAM theorem for the mappings, which implies many previous KAM-type results under some non-degeneracy conditions. Moreover, by this formal KAM theorem, we can also obtain some new interesting results under some weaker non-degeneracy conditions. Thus, the formal KAM theorem can be regarded as a general KAM theorem for areapreserving mappings.

Keywords Area-preserving mapping invariant curve KAM iteration nondegeneracy condition

Corresponding Author(s): Junxiang XU

Issue Date: 21 July 2020

Cite this article:

Kun WANG,Junxiang XU. Existence of invariant curves for area-preserving mappings under weaker non-degeneracy conditions[J]. Front. Math. China, 2020, 15(3): 571-591.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-020-0838-9
https://academic.hep.com.cn/fmc/EN/Y2020/V15/I3/571

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