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

Karen M. Brucks·John Ringland·Charles Tresser
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Abstract

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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Karen M. Brucks, John Ringland, Charles Tresser. 1996-04-02. Organization of parameter space for simple circle maps: the Farey web. https://arxiv.org/abs/math/9604230

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