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

DOI10.1016/S0167-2789(01)00359-1zbMath1098.37502arXivmath/9604230OpenAlexW1979805382MaRDI QIDQ5952614

Karen M. Brucks, John Ringland, Charles Tresser

Publication date: 15 January 2002

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9604230

zbMATH Keywords

dynamics boundariesfrequency-lockingtopological properties

Mathematics Subject Classification ID

Dynamical systems involving maps of the circle (37E10) Dynamical systems involving maps of the interval (37E05) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05)

Cites Work

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• The set of maps \(F_{a,b}:x\mapsto x+a+{b\over 2\pi}\sin(2\pi x)\) with any given rotation interval is contractible
• Existence of periodic points for maps of S\(^1\)
• Genealogy and Bifurcation Skeleton for Cycles of the Iterated Two-Extremum Map of the Interval
• Piecewise linear models for the quasiperiodic transition to chaos
• Rotation orbits and the Farey tree
• A Farey tree organization of locking regions for simple circle maps
• A Genealogy for Finite Kneading Sequences of Bimodal Maps on the Interval
• Small denominators. I. Mappings of the circumference onto itself

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