Sarah Koch

activity

20112022

most citedRoots, Schottky semigroups, and a proof of Bandt's Conjecture

14 citations · 28 across the 12 of their papers we have counts for

collaborators

16 papers

math.DS2022

Totally real points in the Mandelbrot Set

Xavier Buff, Sarah Koch

Recently, Noytaptim and Petsche proved that the only totally real parameters $c \in Q$ for which $f_{c} (z) := z^{2} + c$ is postcritically finite are $0$ , $- 1$ and $- 2$ .…

math.DS2022

On the deck groups of iterates of bicritical rational maps

Sarah Koch, Kathryn Lindsey, Thomas Sharland

Given a rational map $f : C \to C$ on the Riemann sphere, we define $Deck (f)$ to be the group of Möbius transformations $μ$ satisfying $f \…

math.DS2022

Bicritical rational maps with a common iterate

Sarah Koch, Kathryn Lindsey, Thomas Sharland

Let $f$ be a degree $d$ bicritical rational map with critical point set $C_{f}$ and critical value set $V_{f}$ . Using the group $Deck (f^{k})$ of deck transfo…

math.DS2021

Realizing polynomial portraits

William Floyd, Daniel Kim, Sarah Koch +2

It is well known that the dynamical behavior of a rational map $f : C \to C$ is governed by the forward orbits of the critical points of $f$ . The m…

math.DS2018★ 3 cited

Rational maps with a preperiodic critical point

Xavier Buff, Adam L. Epstein, Sarah Koch

We show that the set of conjugacy classes of cubic polynomials with a prefixed critical point, of preperiod $k \geq 1$ , is an irreducible algebraic curve. We also establish an analo…

math.DS2017

On the postcritical set of a rational map

Laura G. DeMarco, Sarah C. Koch, Curtis T. McMullen

The postcritical set $P (f)$ of a rational map $f : P^{1} \to P^{1}$ is the smallest forward invariant subset of $P^{1}$ that contains the critical values of $f$ . In…