Organization of parameter space for simple circle maps: the Farey web

Details Organization of parameter space for simple circle maps: the Farey web Organization of parameter space for simple circle maps: the Farey web

1996-04-02

arxiv.org/abs/math/9604230v1

Mathematics

Dynamical Systems

Scientific paper

We define the Farey web --- a collection of loci in the parameter plane of families of simple non-invertible maps of the circle. We prove some results about the arrangement of these loci and their relationships with other dynamically significant features of the parameter plane. The results enable us to provide short proofs for a number of theorems about the organization of frequency-locking.

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