On the left side derivative of the Hausdorff dimension of the Julia sets for \({z^2+c}\) at \({c=-3/4}\)

DOI10.1007/s11856-014-0001-yzbMath1308.37025OpenAlexW2151606349WikidataQ122998771 ScholiaQ122998771MaRDI QIDQ2017109

Ludwik Jaksztas

Publication date: 25 June 2014

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11856-014-0001-y

zbMATH Keywords

Julia setHausdorff dimensionMandelbrot settransfer operatorhyperbolic componenthyperbolic mapfilled-in Julia setFatou coordinates.

Mathematics Subject Classification ID

Conformal densities and Hausdorff dimension for holomorphic dynamical systems (37F35) Small divisors, rotation domains and linearization in holomorphic dynamics (37F50) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10)

Related Items (3)

The Hausdorff Dimension is Convex on the Left Side of 1/4 ⋮ On the directional derivative of the Hausdorff dimension of quadratic polynomial Julia sets at 1/4 ⋮ On the derivative of the Hausdorff dimension of the Julia sets for \(z^2 + c, c \in \mathbb{R}\) at parabolic parameters with two petals

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Dynamical convergence and polynomial vector fields
• The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets
• Numbertheoretical endomorphisms with \(\sigma\)-finite invariant measure
• Hausdorff dimension and conformal dynamics. II: Geometrically finite rational maps
• Thermodynamic formalism and variations of the Hausdorff dimension of quadratic Julia sets
• On the continuity of Hausdorff dimension of Julia sets and similarity between the Mandelbrot set and Julia sets
• Variations of Hausdorff dimension in the exponential family
• On the derivative of the Hausdorff dimension of the quadratic Julia sets
• On the Hausdorff dimension of a Julia set with a rationally indifferent periodic point
• Absolutely Continuous Invariant Measures for Expansive Rational Maps with Rationally Indifferent Periodic Points
• Ergodic Theory for Markov Fibred Systems and Parabolic Rational Maps
• Hausdorff dimension and conformal dynamics, III: Computation of dimension
• Implosion parabolique et dimension de Hausdorff
• Repellers for real analytic maps
• Harmonic measure and expansion on the boundary of the connectedness locus.

This page was built for publication: On the left side derivative of the Hausdorff dimension of the Julia sets for \({z^2+c}\) at \({c=-3/4}\)