Rational periodic points for quadratic maps

2008/01/30 by Jung Kyu Canci, Canci, J. K.
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0801.4636

openalex publication_date 2008/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K be a number field. Let S be a finite set of places of K containing all the archimedean ones. Let R_S be the ring of S-integers of K. In the present paper we consider endomorphisms of \pro of degree 2, defined over K, with good reduction outside S. We prove that there exist only finitely many such endomorphisms, up to conjugation by \rm PGL₂(R_S), admitting a periodic point in \po of order >3. Also, all but finitely many classes with a periodic point in \po of order 3 are parametrized by an irreducible curve.

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