The Proof of a Conjecture Relating Catalan Numbers to an Averaged Mandelbrot-Mobius Iterated Function
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F21%3A50018379" target="_blank" >RIV/62690094:18470/21:50018379 - isvavai.cz</a>
Result on the web
<a href="https://www.mdpi.com/2504-3110/5/3/92" target="_blank" >https://www.mdpi.com/2504-3110/5/3/92</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3390/fractalfract5030092" target="_blank" >10.3390/fractalfract5030092</a>
Alternative languages
Result language
angličtina
Original language name
The Proof of a Conjecture Relating Catalan Numbers to an Averaged Mandelbrot-Mobius Iterated Function
Original language description
In 2021, Mork and Ulness studied the Mandelbrot and Julia sets for a generalization of the well-explored function eta(lambda)(z)=z(2)+lambda. Their generalization was based on the composition of eta(lambda) with the Mobius transformation mu(z)=1/z at each iteration step. Furthermore, they posed a conjecture providing a relation between the coefficients of (each order) iterated series of mu(eta(lambda)(z)) (at z=0) and the Catalan numbers. In this paper, in particular, we prove this conjecture in a more precise (quantitative) formulation.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Fractal and Fractional
ISSN
2504-3110
e-ISSN
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Volume of the periodical
5
Issue of the periodical within the volume
3
Country of publishing house
CH - SWITZERLAND
Number of pages
10
Pages from-to
"Article Number: 92"
UT code for WoS article
000699652600001
EID of the result in the Scopus database
2-s2.0-85112723274