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The Proof of a Conjecture Relating Catalan Numbers to an Averaged Mandelbrot-Möbius Iterated Function
- Source :
- Fractal and Fractional, Vol 5, Iss 3, p 92 (2021)
- Publication Year :
- 2021
- Publisher :
- MDPI AG, 2021.
-
Abstract
- In 2021, Mork and Ulness studied the Mandelbrot and Julia sets for a generalization of the well-explored function ηλ(z)=z2+λ. Their generalization was based on the composition of ηλ with the Möbius transformation μ(z)=1z at each iteration step. Furthermore, they posed a conjecture providing a relation between the coefficients of (each order) iterated series of μ(ηλ(z)) (at z=0) and the Catalan numbers. In this paper, in particular, we prove this conjecture in a more precise (quantitative) formulation.
Details
- Language :
- English
- ISSN :
- 25043110
- Volume :
- 5
- Issue :
- 3
- Database :
- Directory of Open Access Journals
- Journal :
- Fractal and Fractional
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.8a4eba9ba19401e8b9f3efcdb40a036
- Document Type :
- article
- Full Text :
- https://doi.org/10.3390/fractalfract5030092