SPECIAL CURVES AND POSTCRITICALLY FINITE POLYNOMIALS

By Matthew Baker, Laura De Marco. Forum of Mathematics, Pi, 2012

79 citations recorded by the source corpus.

Abstract We study the postcritically finite maps within the moduli space of complex polynomial dynamical systems. We characterize rational curves in the moduli space containing an infinite number of postcritically finite maps, in terms of critical orbit relations, in two settings: (1) rational curves that are polynomially parameterized; and (2) cubic polynomials defined by a given fixed point multiplier. We offer a conjecture on the general form of algebraic subvarieties in the moduli space of rational maps on ${ \mathbb{P} }^{1} $ containing a Zariski-dense subset of postcritically finite maps.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0169d296d00aec4fd9a579c70f6d52ee844d27bb

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Current trends and open problems in arithmetic dynamics (2018, background): “5 (Dynamical André–Oort Conjecture for One-dimensional Families: Baker–DeMarco, 2013, [8]).”
Bifurcations, intersections, and heights (2014, background): “10 of [Baker and DeMarco 2013] states: the map ft is postcritically finite for a Zariski-dense set of t ∈ V if and only if there are at most N dynamically independent critical points.”