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On the widths of the Arnol’d tongues
Published online by Cambridge University Press: 03 May 2013
Abstract
Let $F: \mathbb{R} \rightarrow \mathbb{R} $ be a real analytic increasing diffeomorphism with
$F- \mathrm{Id} $ being 1-periodic. Consider the translated family of maps
$\mathop{({F}_{t} : \mathbb{R} \rightarrow \mathbb{R} )}\nolimits_{t\in \mathbb{R} } $ defined as
${F}_{t} (x)= F(x)+ t$. Let
$\mathrm{Trans} ({F}_{t} )$ be the translation number of
${F}_{t} $ defined by
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- Copyright ©2013 Cambridge University Press