On the magnification of Cantor sets and their limit models

DOI10.1007/BF01299636zbMath0843.28002OpenAlexW2005898561MaRDI QIDQ1909219

Tim Bedford, Albert Meads Fisher

Publication date: 11 August 1996

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/178710

zbMATH Keywords

fractal setsscaling functioncookie-cutter Cantor setscenery

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Fractals (28A80)

Related Items (7)

Dynamics of the scenery flow and conical density theorems ⋮ Locally rich compact sets ⋮ Self-affine sets with fibred tangents ⋮ Local entropy averages and projections of fractal measures ⋮ Scenery Flow, Conical Densities, and Rectifiability ⋮ Tangent measure distributions of hyperbolic Cantor sets ⋮ Dynamics of the scenery flow and geometry of measures

Cites Work

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• Similarity between the Mandelbrot set and Julia sets
• On the quadratic mapping \(z\rightarrow z^{2}-\mu \) for complex \(\mu \) and \(z\): the fractal structure of its set, and scaling
• An embedding theorem for the Fell topology
• Stieltjes integration and stochastic calculus with respect to self-affine functions
• Fractals and hyperspaces
• Expansive one-parameter flows
• Integer Cantor sets and an order-two ergodic theorem
• Ratio geometry, rigidity and the scenery process for hyperbolic Cantor sets
• A class of deterministic self-affine processes

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