8 citations · 30 across the 14 of their papers we have counts for
16 papers
Julia Sets for Sequences of Monomials
Lubashan Pathirana, Carsten Lunde Petersen, Dimitris Vardakis
We study Julia sets arising from non-autonomous iteration of monomials on the Riemann sphere. We give a precise description of the Julia set associated to an arbitrary sequence of…
Hausdorff limits of external rays: the topological picture
Carsten Lunde Petersen, Saeed Zakeri
We study Hausdorff limits of the external rays of a given periodic angle along a convergent sequence of polynomials of degree with connected Julia sets.
Conformal renormalization of compact sets
Carsten Lunde Petersen, Filip Samuelsen
This paper develops a conformal renormalization scheme for compact sets . As one application of the conformal renormalization scheme we prove that for every i…
The Parabolic Mandelbrot Set
Carsten Lunde Petersen, Pascale Roesch
We solve the longstanding conjecture by Milnor (1993) concerning the connectedness locus of the family of quadratic rational maps tangent to the identity at . We prov…
Filled Julia sets of Chebyshev polynomials
Jacob Stordal Christiansen, Christian Henriksen, Henrik Laurberg Pedersen +1
We study the possible Hausdorff limits of the Julia sets and filled Julia sets of subsequences of the sequence of dual Chebyshev polynomials of a non-polar compact set K in C and c…
Periodic Points and Smooth Rays
Carsten L. Petersen, Saeed Zakeri
Let be a polynomial map with disconnected filled Julia set and let be a repelling or parabolic periodic point of . We show that if t…