Self-similarity of Farey Staircases

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dc.creatorGrynberg, Sebastian
dc.creatorPiacquadio, Maria N.
dc.date2003-06-09
dc.date.accessioned2026-07-07T04:30:15Z
dc.date.available2026-07-07T04:30:15Z
dc.descriptionWe study Cantor Staircases in physics that have the Farey-Brocot arrangement for the Q/P rational heights of stability intervals I(Q/P), and such that the length of I(Q/P)is a convex function of 1/P. Circle map staircases and the magnetization function fall in this category. We show that the fractal sets Ommega underlying these staircases are connected with key sets in Number Theory via their (alpha,f(alpha)) multifractal decomposition spectra. It follows that such sets Ommega are self similar when the usual (Euclidean) measure is replaced by the hyperbolic measure induced by the Farey-Brocot partition.
dc.description20 pages, Latex, 6 figures
dc.identifierhttps://arxiv.org/abs/math-ph/0306024
dc.identifierhttp://arxiv.org/abs/math-ph/0306024
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57409
dc.subjectMathematical Physics
dc.subject11K55
dc.titleSelf-similarity of Farey Staircases
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