Repeated compositions of Möbius transformations

DOI10.1017/etds.2018.43zbMath1475.37051arXiv1609.01261OpenAlexW2964117440MaRDI QIDQ5207985

Matthew Jacques, Ian Short

Publication date: 14 January 2020

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.01261

zbMATH Keywords

Möbius transformationsHausdorff dimensioncomposition sequenceslimit disk type

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) Hausdorff and packing measures (28A78)

Cites Work

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• Compositions of contractions
• On compositions of analytic self-mappings of a convex domain
• Continued fractions. Vol. 1: Convergence theory
• The limiting behavior of sequences of Moebius transformations
• Computing the Hausdorff dimension of subshifts using matrices
• Continued fractions, discrete groups and complex dynamics
• The Hillam-Thron theorem in higher dimensions
• Möbius transformations mapping the unit disk into itself
• Random iteration of analytic maps
• Hausdorff dimension of sets of divergence arising from continued fractions
• Random holomorphic iterations and degenerate subdomains of the unit disk

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