Laura Demarco

activity

20022022

most citedPreperiodic points and unlikely intersections

56 citations · 98 across the 21 of their papers we have counts for

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18 papers · 1 filter

math.DS2022★ 1 cited

Dynamics on $P^{1}$ : preperiodic points and pairwise stability

Laura DeMarco, Niki Myrto Mavraki

In [DKY], it was conjectured that there is a uniform bound $B$ , depending only on the degree $d$ , so that any pair of holomorphic maps $f, g : P^{1} \to P^{1}$ with degr…

math.DS2021

Variation of Canonical Height for Fatou points on $P^{1}$

Laura DeMarco, Niki Myrto Mavraki

Let $f : P^{1} \to P^{1}$ be a map of degree $> 1$ defined over a function field $k = K (X)$ , where $K$ is a number field and $X$ is a projective curve over $K$ . For each…

math.DS2019★ 1 cited

Common preperiodic points for quadratic polynomials

Laura DeMarco, Holly Krieger, Hexi Ye

Let $f_{c} (z) = z^{2} + c$ for $c \in C$ . We show there exists a uniform bound on the number of points in $P^{1} (C)$ that can be preperiodic for both $f_{c_{1}}$ a…

math.DS2017★ 1 cited

Discontinuity of a degenerating escape rate

Laura DeMarco, Yûsuke Okuyama

We look at degenerating meromorphic families of rational maps on $P^{1}$ -- holomorphically parameterized by a punctured disk -- and we provide examples where the bifurcatio…

math.DS2016★ 1 cited

KAWA 2015: Dynamical moduli spaces and elliptic curves

Laura DeMarco

In these lecture notes, we present a connection between the complex dynamics of a family of rational functions $f_{t} : P^{1} \to P^{1}$ , parameterized by $t$ in a Rieman…

math.DS2016

Convex shapes and harmonic caps

Laura DeMarco, Kathryn Lindsey

Any planar shape $P \subset C$ can be embedded isometrically as part of the boundary surface $S$ of a convex subset of $R^{3}$ such that $\partial P$ supports the po…

Dynamics on P1: preperiodic points and pairwise stability