Author:
BAKER MATTHEW,DE MARCO LAURA
Abstract
AbstractWe 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.
Publisher
Cambridge University Press (CUP)
Subject
Discrete Mathematics and Combinatorics,Geometry and Topology,Mathematical Physics,Statistics and Probability,Algebra and Number Theory,Analysis
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