Existence of invariant curves for degenerate almost periodic reversible mappings

Peng Huang

doi:10.3934/dcds.2022074

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2022, Volume 42, Issue 10: 4853-4886. Doi: 10.3934/dcds.2022074

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Existence of invariant curves for degenerate almost periodic reversible mappings

Peng Huang^,

School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China

^*Corresponding author: Peng Huang
^*Corresponding author: Peng Huang

Received: September 30, 2021

Revised: March 31, 2022

Early access: June 2022

Published: September 2022

The author is supported by the National Natural Science Foundation of China (11901131), Guizhou Provincial Science and Technology Foundation ([2020]1Y006)

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Abstract

In this paper we are concerned with the existence of invariant curves for almost periodic reversible mappings with higher order degeneracy of the twist condition. In the proof we use a new variant of the KAM theory, containing an artificial parameter $ q, 0<q<1 $, which makes the steps of the KAM iteration infinitely small in the speed of function $ q^n \varepsilon, $ rather than super exponential function.

Keywords:

Invariant curves,
almost periodic reversible mappings,
higher order degeneracy of the twist condition,
KAM theory.

Mathematics Subject Classification: Primary: 37J40; Secondary: 70H12.

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References

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