Geometry and ergodic theory of non-hyperbolic exponential maps

DOI10.1090/S0002-9947-07-04151-7zbMath1110.37038OpenAlexW2051173830MaRDI QIDQ3433744

Anna Zdunik, Mariusz Urbański

Publication date: 2 May 2007

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-07-04151-7

zbMATH Keywords

Hausdorff dimensionHausdorff measureexponential familypacking measureconformal measureinvariant ergodic measures

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Conformal densities and Hausdorff dimension for holomorphic dynamical systems (37F35) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10)

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Cites Work

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• The exponential map is not recurrent
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• On Sullivan's conformal measures for rational maps of the Riemann sphere
• Packing Measure, and its Evaluation for a Brownian Path
• Geometric measures for parabolic rational maps
• Area and Hausdorff Dimension of Julia Sets of Entire Functions
• Hausdorff dimension of theM-set of λ exp(z)
• Real analyticity of Hausdorff dimension of finer Julia sets of exponential family

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