Logarithmic Capacity and Renormalizability for Landing on the Mandelbrot Set | Zendy

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Logarithmic Capacity and Renormalizability for Landing on the Mandelbrot Set

Author(s) -

Manning Anthony

Publication year - 1996

Publication title -

bulletin of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.396

H-Index - 48

eISSN - 1469-2120

pISSN - 0024-6093

DOI - 10.1112/blms/28.5.521

Subject(s) - mandelbrot set , logarithm , conjecture , mathematics , set (abstract data type) , sequence (biology) , combinatorics , pure mathematics , substitution (logic) , mathematical analysis , computer science , fractal , biology , genetics , programming language

We study renormalizability of external angles of the Mandelbrot set M . Estimates are made of the logarithmic capacity of sets of angles that are infinitely renormalizable with a specific sequence of periods, using a substitution due to Douady. These show that many of the infinitely renormalizable rays do land on M , which provides further evidence in support of the conjecture that M is locally connected.

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