On the invariant sets of a family of quadratic maps

DOI10.1007/BF01211955zbMath0535.30024OpenAlexW2009727276MaRDI QIDQ790987

Andrew N. Harrington, Michael F. Barnsley, Jeffrey S. Geronimo

Publication date: 1983

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01211955

zbMATH Keywords

Julia setCantor setHausdorff dimensionnormal familyChebyshev polynomial

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Ergodic theory (37A99)

Related Items (18)

Infinite-Dimensional Jacobi Matrices Associated with Julia Sets ⋮ A family of almost periodic Schrödinger operators ⋮ Mellin transforms associated with Julia sets and physical applications ⋮ Moments of Balanced Measures on Julia Sets ⋮ Complex analytic dynamics on the Riemann sphere ⋮ Condensed Julia Sets, with an Application to a Fractal Lattice Model Hamiltonian ⋮ Taylor series approximations to Julia set scaling functions ⋮ Orthogonal Polynomials with Respect to Self-Similar Measures ⋮ Orthogonal polynomials on the unit circle via a polynomial mapping on the real line ⋮ Orthogonality properties of iterated polynomial mappings ⋮ Physical meaning for Mandelbrot and Julia sets ⋮ Unnamed Item ⋮ Some tree-like Julia sets and Padé approximants ⋮ Orthogonal polynomials associated with invariant measures on Julia sets ⋮ A review of recent work on almost periodic differential and difference operators ⋮ Geometry, electrostatic measure and orthogonal polynomials on Julia sets for polynomials ⋮ Almost periodic Jacobi matrices associated with Julia sets for polynomials ⋮ Geometry and combinatorics of Julia sets of real quadratic maps

Cites Work

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• Absolutely continuous invariant measures for one-parameter families of one-dimensional maps
• Quantitative universality for a class of nonlinear transformations
• Invariant sets under iteration of rational functions
• Scattering Theory and Polynomials Orthogonal on the Real Line
• The Diophantine moment problem and the analytic structure in the activity of the ferromagnetic Ising model
• Orthogonal polynomials associated with invariant measures on Julia sets
• Ergodic and Mixing Properties of Chebyshev Polynomials

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