Geometric measures for parabolic rational maps

DOI10.1017/S014338570000657XzbMath0737.58030MaRDI QIDQ3363358

Mariusz Urbański, Manfred Denker

Publication date: 1992

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

Hausdorff measurepacking measurerational maps

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Ergodic theory (37A99) Hausdorff and packing measures (28A78)

Related Items

On the existence of conformal measures supported on conical points. ⋮ Fractal dimensions for Jarník limit sets of geometrically finite Kleinian groups; the semi-classical approach ⋮ Geometry and ergodic theory of parabolic meromorphic functions ⋮ The finer geometry and dynamics of the hyperbolic exponential family ⋮ On conformal measures of parabolic meromorphic functions ⋮ Hausdorff measures on Julia sets of subexpanding rational maps ⋮ The capacity of parabolic Julia sets ⋮ Fractal measures for parabolic IFS ⋮ Equilibriums of some non-Hölder potentials ⋮ Measures and dimensions in conformal dynamics ⋮ ON HAUSDORFF MEASURES AND SBR MEASURES FOR PARABOLIC RATIONAL MAPS ⋮ Self-similar sets of zero Hausdorff measure and positive packing measure ⋮ Geometry and ergodic theory on non-recurrent elliptic functions ⋮ Geometry and ergodic theory of non-hyperbolic exponential maps ⋮ Thermodynamic Formalism and Geometric Applications for Transcendental Meromorphic and Entire Functions

Cites Work

• Unnamed Item
• Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups
• Differentiation of integrals in \(\mathbb{R}^n\)
• Invariant sets under iteration of rational functions
• Complex analytic dynamics on the Riemann sphere
• Hausdorff and Conformal Measures on Julia Sets with a Rationally Indifferent Periodic Point