Jack Burkart

activity

20172024

most citedTranscendental Julia Sets of Minimal Hausdorff Dimension

1 citations · 1 across the 5 of their papers we have counts for

collaborators

6 papers

math.CV2024

Interpolating quasiregular power mappings

Jack Burkart, Alastair N. Fletcher, Daniel A. Nicks

We construct a quasiregular mapping in $R^{3}$ that is the first to illustrate several important dynamical properties: the quasi-Fatou set contains wandering components; the…

math.CV2021★ 1 cited

Transcendental Julia Sets of Minimal Hausdorff Dimension

Jack Burkart, Kirill Lazebnik

We show the existence of transcendental entire functions $f : C \to C$ with Hausdorff-dimension $1$ Julia sets, such that every Fatou component of $f$ has…

math.CV2021

Interpolation of Power Mappings

Jack Burkart, Kirill Lazebnik

Let $(M_{j})_{j = 1}^{\infty} \in N$ and $(r_{j})_{j = 1}^{\infty} \in R^{+}$ be increasing sequences satisfying some mild rate of growth conditions. We prove that there is an enti…

math.CV2020

A Jordan Curve that cannot be Crossed by Rectifiable Arcs on a Set of Zero Length

Jack Burkart

We construct a Jordan curve $Γ \subset C$ so that for any rectifiable arc $σ$ with endpoints in distinct complementary components of $Γ$ , $H^{1} (σ \cap Γ) > 0$ .

math.CV2019

Transcendental Julia Sets with Fractional Packing Dimension

Jack Burkart

We construct a family of transcendental entire functions whose Julia sets have packing dimension in $(1, 2)$ . These are the first examples where the computed packing dimension is no…

math.AP2017

A Differential Harnack Inequality for the Newell-Whitehead Equation

Derek Booth, Jack Burkart, Xiaodong Cao +4

This paper will develop a Li-Yau-Hamilton type differential Harnack estimate for positive solutions to the Newell-Whitehead equation on $R^{n}$ . We then use our LYH-differen…