Torsion of instability zones for conservative twist maps on the annulus

For a twist map f of the annulus preserving the Lebesgue measure, we give sufficient conditions to assure the existence of a set of positive measure of points with non-zero asymptotic torsion. In particular, we deduce that every bounded instability region for f contains a set of positive measure of...

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Bibliographic Details
Published in:Nonlinearity 2021-01, Vol.34 (1), p.411-423
Main Authors: Florio, Anna, Le Calvez, Patrice
Format: Article
Language:English
Subjects:
conservative twist map
Mathematics
torsion
twist map
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Summary:For a twist map f of the annulus preserving the Lebesgue measure, we give sufficient conditions to assure the existence of a set of positive measure of points with non-zero asymptotic torsion. In particular, we deduce that every bounded instability region for f contains a set of positive measure of points with non-zero asymptotic torsion. Moreover, for an exact symplectic twist map f, we provide a simple, geometric proof of a result by Cheng and Sun (1996 Sci. China A 39 709) which characterizes C0-integrability of f by the absence of conjugate points.
ISSN:0951-7715
1361-6544
DOI:10.1088/1361-6544/abbe63