10 citations · 39 across the 9 of their papers we have counts for
12 papers
Thurston's pullback map, invariant covers, and the global dynamics on curves
Mario Bonk, Mikhail Hlushchanka, Russell Lodge
We consider rational maps on the Riemann sphere with an -invariant set of four marked points containing the postcrit…
On Deformation Space Analogies between Kleinian Reflection Groups and Antiholomorphic Rational Maps
Russell Lodge, Yusheng Luo, Sabyasachi Mukherjee
In a previous paper, we constructed an explicit dynamical correspondence between certain Kleinian reflection groups and certain anti-holomorphic rational maps on the Riemann sphere…
Iterated monodromy groups of rational functions and periodic points over finite fields
Andrew Bridy, Rafe Jones, Gregory Kelsey +1
Let be a prime power and a rational function with coefficients in a finite field . For , each element of $\mathbb{P}^1(\F_{q^n})$ is either periodic…
Circle packings, kissing reflection groups and critically fixed anti-rational maps
Russell Lodge, Yusheng Luo, Sabyasachi Mukherjee
In this paper, we establish an explicit correspondence between kissing reflection groups and critically fixed anti-rational maps. The correspondence, which is expressed using simpl…
On Dynamical Gaskets Generated by Rational Maps, Kleinian Groups, and Schwarz Reflections
Russell Lodge, Mikhail Lyubich, Sergei Merenkov +1
According to the Circle Packing Theorem, any triangulation of the Riemann sphere can be realized as a nerve of a circle packing. Reflections in the dual circles generate a Kleinian…
Puzzles and the Fatou-Shishikura injection for rational Newton maps
Kostiantyn Drach, Russell Lodge, Dierk Schleicher +1
We establish a principle that we call the Fatou-Shishikura injection for Newton maps of polynomials: there is a dynamically natural injection from the set of non-repelling periodic…
Invisible Tricorns in Real Slices of Rational Maps
Russell Lodge, Sabyasachi Mukherjee
One of the conspicuous features of real slices of bicritical rational maps is the existence of Tricorn-type hyperbolic components. Such a hyperbolic component is called invisible i…
Quadratic Thurston maps with few postcritical points
Gregory Kelsey, Russell Lodge
We use the theory of self-similar groups to enumerate all combinatorial classes of non-exceptional quadratic Thurston maps with fewer than five postcritical points. The enumeration…
Origami, affine maps, and complex dynamics
William Floyd, Gregory Kelsey, Sarah Koch +4
We investigate the combinatorial and dynamical properties of so-called nearly Euclidean Thurston maps, or NET maps. These maps are perturbations of many-to-one folding maps of an a…
A classification of postcritically finite Newton maps
Russell Lodge, Yauhen Mikulich, Dierk Schleicher
The dynamical classification of rational maps is a central concern of holomorphic dynamics. Much progress has been made, especially on the classification of polynomials and some ap…
Combinatorial properties of Newton maps
Russell Lodge, Yauhen Mikulich, Dierk Schleicher
This paper constructs a combinatorial model for all postcritically finite rational maps arising as the Newton's method of a complex polynomial. This model is used in [LMS] to give…
Boundary Values of the Thurston Pullback Map
Russell Lodge
For any Thurston map with exactly four postcritical points, we present an algorithm to compute the Weil-Petersson boundary values of the corresponding Thurston pullback map. This p…