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August, 2022 Existence of Invariant Curves for Degenerate Quasi-periodic Reversible Mappings
Peng Huang
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Taiwanese J. Math. 26(4): 765-798 (August, 2022). DOI: 10.11650/tjm/220201

Abstract

In this paper we are concerned with the existence of invariant curves of quasi-periodic reversible mappings with higher order degeneracy of the twist condition under the Brjuno–Rüssmann's non-resonant condition. In the proof we use a new variant of the KAM theory, containing an artificial parameter $q$, $0 \lt q \lt 1$, which makes the steps of the KAM iteration infinitely small in the speed of function $q^n \varepsilon$, rather than super exponential function.

Funding Statement

This pape was partially supported by the National Natural Science Foundation of China (11901131), Guizhou Provincial Science and Technology Foundation ([2020]1Y006).

Citation

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Peng Huang. "Existence of Invariant Curves for Degenerate Quasi-periodic Reversible Mappings." Taiwanese J. Math. 26 (4) 765 - 798, August, 2022. https://doi.org/10.11650/tjm/220201

Information

Received: 20 October 2021; Revised: 8 February 2022; Accepted: 11 February 2022; Published: August, 2022
First available in Project Euclid: 23 February 2022

Digital Object Identifier: 10.11650/tjm/220201

Subjects:
Primary: 37J40 , 70K43

Keywords: Brjuno–Rüssmann's non-resonant condition , higher order degeneracy of the twist condition , invariant curves , KAM theory , quasi-periodic reversible mappings

Rights: Copyright © 2022 The Mathematical Society of the Republic of China

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Vol.26 • No. 4 • August, 2022
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