Twist interval for twist maps

Pengfei Zhang

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arXiv · 1805.11086

Twist interval for twist maps

Pengfei Zhang

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Abstract

The twist interval of a twist map on the annulus $A=\mathbb{T}\times [0,1]$ has nonempty interior if $f$ preserves the area, but could be degenerate for general twist maps. In this note, we show that if a twist map $f$ is non-wandering, then the twist interval of $f$ is non-degenerate. Moreover, if there are two disjoint invariant curves of $f$, then their rotation numbers must be different (no matter if they are rational or irrational).

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Pengfei Zhang. 2018-05-28. Twist interval for twist maps. https://arxiv.org/abs/1805.11086

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