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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 92, p 92 (2021), Fractal and Fractional, Volume 5, Issue 3
- 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.
- Subjects :
- Statistics and Probability
Generalization
MathematicsofComputing_GENERAL
Julia set
Mandelbrot set
iterated function
Combinatorics
Catalan number
fractal
QA1-939
Mathematics
QA299.6-433
Conjecture
Series (mathematics)
Möbius transformation
Statistical and Nonlinear Physics
Function (mathematics)
TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES
Iterated function
Thermodynamics
Catalan numbers
QC310.15-319
Analysis
Subjects
Details
- ISSN :
- 25043110
- Volume :
- 5
- Database :
- OpenAIRE
- Journal :
- Fractal and Fractional
- Accession number :
- edsair.doi.dedup.....641d35c5372d3e7b8a44f09782b34bd7