Dimension rigidity in conformal structures

DOI10.1016/j.aim.2016.12.034zbMath1405.37047arXiv1504.01774OpenAlexW2137564842MaRDI QIDQ507241

Tushar Das, David Simmons, Mariusz Urbański

Publication date: 3 February 2017

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.01774

zbMATH Keywords

Julia setsHausdorff dimensionKleinian groupsrectifiabilitygeometric measure theoryiterated function systemsconformal dynamicsdimension rigidityiteration of rational functions

Mathematics Subject Classification ID

Conformal densities and Hausdorff dimension for holomorphic dynamical systems (37F35) Small divisors, rotation domains and linearization in holomorphic dynamics (37F50) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) Fractals (28A80) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10)

Related Items (5)

On the dimension spectra of infinite conformal iterated function systems ⋮ A new perspective on the Sullivan dictionary via Assouad type dimensions and spectra ⋮ Asymptotic solution of Bowen equation for perturbed potentials on shift spaces with countable states ⋮ Hausdorff dimensions of perturbations of a conformal iterated function system via thermodynamic formalism ⋮ Extremality and dynamically defined measures, part II: Measures from conformal dynamical systems

Cites Work

• Hausdorff dimension of limit sets for parabolic IFS with overlaps.
• The analysis of additive set functions in Euclidean space
• Homological dimension and critical exponent of Kleinian groups
• Subsets of rectifiable curves in Hilbert space-the analyst's TSP
• Hausdorff dimension of harmonic measure on the boundary of an attractive basin for a holomorphic map
• Quasiconformal homeomorphisms and dynamics. I: Solution of the Fatou- Julia problem on wandering domains
• Hausdorff dimension of quasi-circles
• The density at infinity of a discrete group of hyperbolic motions
• The limit set of a Fuchsian group
• Complex dynamics
• Patterson-Sullivan measures on the boundary of a hyperbolic space in the sense of Gromov
• Kleinian groups with small limit sets
• Exotic actions of free Kleinian groups
• Hausdorff dimension and Kleinian groups
• Non-rectifiable limit sets of dimension one.
• Rectifiable sets in metric and Banach spaces
• Hausdorff dimension and conformal dynamics. II: Geometrically finite rational maps
• Parabolic orbifolds and the dimension of the maximal measure for rational maps
• A Kaluza-Klein approach to hyperbolic three-manifolds
• Further remarks on the exponent of convergence of Poincaré series
• Length of Julia curves
• Geometrical finiteness for hyperbolic groups
• Generalization of a construction of Antoine
• Rational maps with real multipliers
• Bowen’s formula for meromorphic functions
• Graph directed Markov systems on Hilbert spaces
• On the Hausdorff dimension of a Julia set with a rationally indifferent periodic point
• Thermodynamical formalism and multifractal analysis for meromorphic functions of finite order
• Equilibrium states in negative curvature
• Hyperbolic dimension and radial Julia sets of transcendental functions
• Meromorphic functions with linearly distributed values and Julia sets of rational functions
• A Wild Cantor Set as the Limit Set of a Conformal Group Action on S 3
• Discrete conformal groups and measurable dynamics
• Hausdorff Dimension of Wild Fractals
• Demension and Measure
• Elements of Lipschitz topology
• Conical limit set and Poincaré exponent for iterations of rational functions
• Rational functions with no recurrent critical points
• Rectifiable Julia Curves
• Finer geometric rigidity of limit sets of conformal IFS
• Parabolic iterated function systems
• Measures and dimensions in conformal dynamics
• Equality of pressures for rational functions
• Dimensions and Measures in Infinite Iterated Function Systems
• Renormalization and 3-Manifolds Which Fiber over the Circle
• Statistical properties of one-dimensional maps under weak hyperbolicity assumptions
• Statistical properties of topological Collet–Eckmann maps
• Tangled Embeddings of One-Dimensional Continua
• Ein eindimensionales Kompaktum in $E^3$, das sich nicht lagetreu in die Mengersche Universalkurve einbetten läβt
• Dimension and Measure
• Divergence groups have the Bowen property
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