An embedding of the Farey web in the parameter space of simple families of circle maps

Karen Brucks; John Ringland; Charles Tresser

doi:10.1016/S0167-2789(01)00359-1

An embedding of the Farey web in the parameter space of simple families of circle maps

Karen Brucks
, John Ringland
, Charles Tresser

Mathematics

University of Wisconsin-Milwaukee
IBM

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

An embedding of the Farey web, which is an extension of Farey tree, is described in the parameter space of simple circle maps. The effects of the embedding on the organization of frequency-locking and topological properties of the boundary between simple and complicated dynamics are discussed. A smooth Farey web is constructed and the results are stated in terms of the standard sine family.

Original language	English
Pages (from-to)	142-162
Number of pages	21
Journal	Physica D: Nonlinear Phenomena
Volume	161
Issue number	3-4
DOIs	https://doi.org/10.1016/S0167-2789(01)00359-1
State	Published - Jan 15 2002

Keywords

Circle maps
Farey web
Parameter space

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10.1016/S0167-2789(01)00359-1

Cite this

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abstract = "An embedding of the Farey web, which is an extension of Farey tree, is described in the parameter space of simple circle maps. The effects of the embedding on the organization of frequency-locking and topological properties of the boundary between simple and complicated dynamics are discussed. A smooth Farey web is constructed and the results are stated in terms of the standard sine family.",

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AU - Brucks, Karen

AU - Ringland, John

AU - Tresser, Charles

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N2 - An embedding of the Farey web, which is an extension of Farey tree, is described in the parameter space of simple circle maps. The effects of the embedding on the organization of frequency-locking and topological properties of the boundary between simple and complicated dynamics are discussed. A smooth Farey web is constructed and the results are stated in terms of the standard sine family.

AB - An embedding of the Farey web, which is an extension of Farey tree, is described in the parameter space of simple circle maps. The effects of the embedding on the organization of frequency-locking and topological properties of the boundary between simple and complicated dynamics are discussed. A smooth Farey web is constructed and the results are stated in terms of the standard sine family.

KW - Circle maps

KW - Farey web

KW - Parameter space

UR - https://www.scopus.com/pages/publications/0037080082

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DO - 10.1016/S0167-2789(01)00359-1

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JO - Physica D: Nonlinear Phenomena

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IS - 3-4

ER -

An embedding of the Farey web in the parameter space of simple families of circle maps

Abstract

Keywords

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