A Moser theorem for multiscale mappings

Xuefeng Zhao; Yong Li

doi:10.3934/dcds.2022037

Article Contents

2022, Volume 42, Issue 8: 3931-3951. Doi: 10.3934/dcds.2022037

This issue Previous Article Singular solutions of some elliptic equations involving mixed absorption-reaction Next Article Gibbs measures for hyperbolic attractors defined by densities

A Moser theorem for multiscale mappings

Xuefeng Zhao^1, and
Yong Li^1,2, ,

1.
College of Mathematics, Jilin University, Changchun 130012, China
2.
School of Mathematics and Statistics, and Center for Mathematics, and Interdisciplinary Sciences, Northeast Normal University, Changchun, 130024, China

^*Corresponding author: Yong Li
^*Corresponding author: Yong Li

Received: September 2021

Revised: January 2022

Early access: April 2022

Published: August 2022

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Abstract

In this paper, we study the persistence of invariant tori in nearly integrable multiscale twist mappings with intersection property and high degeneracy in the integrable part. Such results are also presented for the mappings with distinct number of angles and actions, which affirms the existence of lower-dimensional invariant tori in such mappings. Hence we establish a Moser's theorem in multiscales.

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Mathematics Subject Classification: 37E40, 37J40, 70H08.

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References

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