Generic standard-like forcings with k>=3 breakpoints, and generic Lipschitz and C^r forcings, have no pinched rational Arnol'd tongues.
Campbell, Roza Galeeva, Charles Tresser, and David J
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Pinched Arnol'd tongues for Families of circle maps
Generic standard-like forcings with k>=3 breakpoints, and generic Lipschitz and C^r forcings, have no pinched rational Arnol'd tongues.