Thermodynamic formalism and variations of the Hausdorff dimension of quadratic Julia sets

DOI10.1007/s002200050778zbMath0985.37043OpenAlexW2065307815WikidataQ123022594 ScholiaQ123022594MaRDI QIDQ1976646

Michel Zinsmeister, Guillaume Havard

Publication date: 10 May 2000

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

Full work available at URL: https://doi.org/10.1007/s002200050778

zbMATH Keywords

Julia setHausdorff dimensionquadratic family

Mathematics Subject Classification ID

Small divisors, rotation domains and linearization in holomorphic dynamics (37F50) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Hausdorff and packing measures (28A78)

Related Items (9)

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 -2 ⋮ Hausdorff dimension of Julia sets in the logistic family ⋮ On the directional derivative of the Hausdorff dimension of quadratic polynomial Julia sets at 1/4 ⋮ Simple proofs for the derivative estimates of the holomorphic motion near two boundary points of the Mandelbrot set ⋮ Continuity of Hausdorff dimension of Julia-Lavaurs sets as a function of the phase ⋮ On the left side derivative of the Hausdorff dimension of the Julia sets for \({z^2+c}\) at \({c=-3/4}\) ⋮ 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 ⋮ On the derivative of the Hausdorff dimension of the quadratic Julia sets

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