@article{trojovský_venkatachalam_2021, 
  title={The Proof of a Conjecture Relating Catalan Numbers to an Averaged Mandelbrot-Möbius Iterated Function}, 
  DOI={10.3390/fractalfract5030092}, 
  abstractNote={<jats:p>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.</jats:p>}, 
  publisher={MDPI AG}, 
  author={Trojovský, Pavel and Venkatachalam}, 
  year={2021}, 
  month={Aug}
  }