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Start Over Descriptor "Julia set" Search Limiters Available in Library Collection Topic binomial coefficients Publication Year Range Last 50 years

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1 results on '"Julia set"'

1. The Proof of a Conjecture Relating Catalan Numbers to an Averaged Mandelbrot-Möbius Iterated Function.

Author

Trojovský, Pavel and Venkatachalam, K.

Subjects
*ITERATIVE methods (Mathematics), *LOGICAL prediction, *COEFFICIENTS (Statistics), *BINOMIAL coefficients, *MATHEMATICAL analysis
Abstract

In 2021, Mork and Ulness studied the Mandelbrot and Julia sets for a generalization of the well-explored function hl(z) = z2 +l. Their generalization was based on the composition of hl with the Möbius transformation m(z) = 1z at each iteration step. Furthermore, they posed a conjecture providing a relation between the coefficients of (each order) iterated series of m(hl(z)) (at z = 0) and the Catalan numbers. In this paper, in particular, we prove this conjecture in a more precise (quantitative) formulation. [ABSTRACT FROM AUTHOR]

Published
2021
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