Frontiers in complex dynamics

DOI10.1090/S0273-0979-1994-00519-1zbMath0807.30013arXivmath/9410221OpenAlexW2170400369MaRDI QIDQ4310793

Publication date: 2 March 1995

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

Full work available at URL: https://arxiv.org/abs/math/9410221

zbMATH Keywords

polynomials critical points Julia set renormalization rational function hyperbolic Mandelbrot set

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Dynamical systems over complex numbers (37F99)

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Cites Work