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SPECIAL CURVES AND POSTCRITICALLY FINITE POLYNOMIALS

  • MATTHEW BAKER (a1) and LAURA DE MARCO (a2)
Abstract
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.

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The online version of this article is published within an Open Access environment subject to the conditions of the Creative Commons Attribution licence <http://creativecommons.org/licenses/by/3.0/>.
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[BD] M. Baker and L. DeMarco , ‘Preperiodic points and unlikely intersections’, Duke Math. J. 159 (2011), 129.

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Forum of Mathematics, Pi
  • ISSN: -
  • EISSN: 2050-5086
  • URL: /core/journals/forum-of-mathematics-pi
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