Collet, Eckmann and the bifurcation measure

DOI10.1007/s00222-019-00874-5zbMath1477.37053arXiv1705.06114OpenAlexW2964032116MaRDI QIDQ2316825

Matthieu Astorg, Gabriel Vigny, Thomas Gauthier, Nicolae Mihalache

Publication date: 7 August 2019

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.06114

zbMATH Keywords

moduli spacerational mapsCollet-Eckmann rational mapsmaximal bifurcations

Mathematics Subject Classification ID

Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Bifurcations; parameter spaces in holomorphic dynamics; the Mandelbrot and Multibrot sets (37F46) Teichmüller theory; moduli spaces of holomorphic dynamical systems (37F34)

Related Items (10)

Parabolic bifurcation loci in the spaces of rational functions ⋮ Sublinear measures, Menger curvature, and Hausdorff dimension ⋮ Higher bifurcations for polynomial skew products ⋮ Summability condition and rigidity for finite type maps ⋮ Non-statistical rational maps ⋮ Dynamical pairs with an absolutely continuous bifurcation measure ⋮ Geometric methods in holomorphic dynamics ⋮ Fixed points of the Ruelle–Thurston operator and the Cauchy transform ⋮ The bifurcation measure has maximal entropy ⋮ Parametric Lyapunov exponents

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