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Pinched Arnol'd tongues for Families of circle maps
We prove that generically for a family of circle maps \begin{equation*} f_{b, ω} (x) = x + ω+ b\, ϕ(x) \end{equation*} with $ϕ$ a piecewise linear forcing with $k>2$ breakpoints there is no pinching in any of its Arnol'd tongues. This is in contrast to a theorem of Campbell, Galeeva, Tresser, and Uh
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