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Gevrey Smoothness of Families of Invariant Curves for Analytic Area Preserving Mappings

Gevrey Smoothness of Families of Invariant Curves for Analytic Area Preserving Mappings In this paper we prove the existence of a Gevrey family of invariant curves for analytic area preserving mappings. The Gevrey smoothness is expressed by Gevrey index. We specifically obtain the Gevrey index of families of invariant curves which is related to the smoothness of area preserving mappings and the exponent of small divisors condition. Moreover, we obtain a Gevrey normal form of area preserving mappings in a neighborhood of the union of the invariant curves. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Gevrey Smoothness of Families of Invariant Curves for Analytic Area Preserving Mappings

Acta Applicandae Mathematicae , Volume 154 (1) – Nov 9, 2017

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References (34)

Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer Science+Business Media B.V., part of Springer Nature
Subject
Mathematics; Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Classical Mechanics
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/s10440-017-0131-4
Publisher site
See Article on Publisher Site

Abstract

In this paper we prove the existence of a Gevrey family of invariant curves for analytic area preserving mappings. The Gevrey smoothness is expressed by Gevrey index. We specifically obtain the Gevrey index of families of invariant curves which is related to the smoothness of area preserving mappings and the exponent of small divisors condition. Moreover, we obtain a Gevrey normal form of area preserving mappings in a neighborhood of the union of the invariant curves.

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: Nov 9, 2017

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