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The Proof of a Conjecture Relating Catalan Numbers to an Averaged Mandelbrot-Möbius Iterated Function.
- Source :
-
Fractal & Fractional . Sep2021, Vol. 5 Issue 3, p1-10. 10p. - Publication Year :
- 2021
-
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]
Details
- Language :
- English
- ISSN :
- 25043110
- Volume :
- 5
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Fractal & Fractional
- Publication Type :
- Academic Journal
- Accession number :
- 152757994
- Full Text :
- https://doi.org/10.3390/fractalfract5030092