The capacity of parabolic Julia sets

DOI10.1007/BF02571418zbMath0763.30009WikidataQ121864836 ScholiaQ121864836MaRDI QIDQ1204282

Manfred Denker, Mariusz Urbański

Publication date: 3 March 1993

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/174431

zbMATH Keywords

Julia setHausdorff dimensionconformal measure

Mathematics Subject Classification ID

Entropy and other invariants (28D20) Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Hausdorff and packing measures (28A78) Dynamical systems over complex numbers (37F99)

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The parabolic map \(f_{1/e}(z)=\frac{1}{e}e^z\). ⋮ Fractal dimensions for Jarník limit sets of geometrically finite Kleinian groups; the semi-classical approach ⋮ Rational functions with no recurrent critical points ⋮ Geometry and ergodic theory of parabolic meromorphic functions ⋮ A new perspective on the Sullivan dictionary via Assouad type dimensions and spectra ⋮ Hausdorff dimension of quadratic rational Julia sets ⋮ Iterations of holomorphic Collet-Eckmann maps: conformal and invariant measures. Appendix: On non-renormalizable quadratic polynomials ⋮ Measures and dimensions in conformal dynamics ⋮ Geometry and ergodic theory on non-recurrent elliptic functions ⋮ Thermodynamic Formalism and Geometric Applications for Transcendental Meromorphic and Entire Functions

Cites Work

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• Absolutely Continuous Invariant Measures for Expansive Rational Maps with Rationally Indifferent Periodic Points
• Ergodic Theory for Markov Fibred Systems and Parabolic Rational Maps