Generic families of circle diffeomorphisms have parameters with irrational rotation numbers that are limits of parameters possessing arbitrarily large finite numbers of periodic orbits.
Sotomayor, Generic bifurcations of dynamical systems
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Generic families of circle diffeomorphisms have many coexisting periodic orbits
Generic families of circle diffeomorphisms have parameters with irrational rotation numbers that are limits of parameters possessing arbitrarily large finite numbers of periodic orbits.