Equidistribution of the zeros of higher order derivatives in polynomial dynamics

DOI10.1007/s12220-023-01436-1zbMath1530.39016arXiv2309.03296OpenAlexW4387946284MaRDI QIDQ6084646

Yûsuke Okuyama

Publication date: 6 November 2023

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2309.03296

zbMATH Keywords

equidistributioncomplex dynamicsAbel equationhigher order derivativesiterated polynomialSchröder equation

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Iteration theory, iterative and composite equations (39B12) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Functional equations for complex functions (39B32)

Cites Work

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• Invariant sets under iteration of rational functions
• Equidistribution towards the Green current for holomorphic maps
• An invariant measure for rational maps
• Value distribution for sequences of rational mappings and complex dynamics
• Distribution of points with prescribed derivative in polynomial dynamics
• Value distribution of derivatives in polynomial dynamics
• Value distribution of the sequences of the derivatives of iterated polynomials
• Dynamics in One Complex Variable. (AM-160)

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