3 papers
math.DS2025
Lemon limbs of the cubic connectedness locus
Carsten Lunde Petersen, Saeed Zakeri
We describe a primary limb structure in the connectedness locus of complex cubic polynomials, where the limbs are indexed by the periodic points of the doubling map $t \mapsto 2t \…
math.DS2024
Buff forms and invariant curves of near-parabolic maps
Carsten Lunde Petersen, Saeed Zakeri
We introduce a general framework to study the local dynamics of near-parabolic maps using the meromorphic -form introduced by X.~Buff. As a sample application of this setup, we…
math.DS2023
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.