Philip L. Boyland

Pinched Arnol’d tongues for families of circle maps

Abstract We prove that generically for a family of circle maps f b , ω ( x ) = x + ω + b ϕ ( x ) 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 Uherka...