Sarah Koch

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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

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14 papers · 1 filter

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…