In this paper we will study families of circle maps of the form $x\mapsto x+2\pi r + a f(x) \pmod{2\pi}$ and investigate how many periodic trajectories maps from this family can have for a "typical" function $f$ provided the parameter $a$ is small.
Scalings in circle maps III
Asymptotic likelihood of chaos for smooth families of circle maps
Hyperbolicity of renormalization of circle maps with a break-type singularity
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