Special Curves and Postcritically Finite Polynomials
نویسندگان
چکیده
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 P1 containing a Zariski-dense subset of postcritically finite maps. 2010 Mathematics Subject Classification: 37F45 (primary); 11G50, 30C10 (secondary)
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1 UMR 8628 CNRS, Université Paris-Sud, F-91405 Orsay, France. Current address: IHES, F-91440 Bures-sur-Yvette, France; e-mail: [email protected] 2 Department of Mathematics, Queens College CUNY, Flushing, New York 11367; Department of Mathematics, CUNY Graduate School, New York, New York 10016; e-mail: [email protected] 3 Département des Mathématiques, Université de Cergy-Pontoise, F-95302 C...
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