THE GEOMETRY OF FAREY STAIRCASES

DOI10.1142/S0218127404011855zbMath1072.37022MaRDI QIDQ5311832

M. Piacquadio Losada

Publication date: 29 August 2005

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

zbMATH Keywords

hyperbolic geometrymultifractal analysisFarey treeCantor staircases

Mathematics Subject Classification ID

Fractals (28A80) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Farey sequences; the sequences (1^k, 2^k, dots) (11B57) Dimension theory of smooth dynamical systems (37C45)

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Multifractal spectrum of an experimental (video feedback) Farey tree

Cites Work

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• Ising models on the Lobachevsky plane
• The scaling of Arnol'd tongues for differentiable homeomorphisms of the circle
• The geometry of Markoff numbers
• Diophantine approximation on hyperbolic Riemann surfaces
• Non-euclidean geometry, continued fractions, and ergodic theory
• Multifractal decompositions of Moran fractals
• Inversion formula for continuous multifractals
• A polynomial time algorithm for the Hausdorff dimension of continued fraction Cantor sets
• Über die Heckeschen Gruppen \({\mathfrak G}(\lambda)\)
• A class of continued fractions associated with certain properly discontinuous groups
• Approach to Markoff's minimal forms through modular functions
• Exceptions to the multifractal formalism for discontinuous measures
• Periodic orbit theory in classical and quantum mechanics
• Cantor Staircases in Physics and Diophantine Approximations
• MULTIFRACTAL SPECTRUM AND THERMODYNAMICAL FORMALISM OF THE FAREY TREE

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