On Poonen's conjecture concerning rational preperiodic points of quadratic maps

DOI10.1216/RMJ-2013-43-1-193zbMath1316.37042arXiv0909.5050OpenAlexW2962784668WikidataQ122949375 ScholiaQ122949375MaRDI QIDQ1951351

Patrick Ingram, Benjamin Hutz

Publication date: 5 June 2013

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.5050

zbMATH Keywords

uniform boundednessquadratic polynomialsperiodic pointsMorton-Silverman conjecturePoonen's conjecture

Mathematics Subject Classification ID

Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps (37P05) Arithmetic properties of periodic points (37P35)

Related Items (13)

A Galois-dynamics correspondence for unicritical polynomials ⋮ Preperiodic points for quadratic polynomials with small cycles over quadratic fields ⋮ Bounds for preperiodic points for maps with good reduction ⋮ New families satisfying the dynamical uniform boundedness principle over function fields ⋮ Quadratic rational functions with a rational periodic critical point of period 3 ⋮ Dynamical modular curves for quadratic polynomial maps ⋮ Preperiodic points for rational functions defined over a global field in terms of good reduction ⋮ Finite orbit points for sets of quadratic polynomials ⋮ Scarcity of finite orbits for rational functions over a number field ⋮ Benedetto’s trick and existence of rational preperiodic structures for quadratic polynomials ⋮ Determination of all rational preperiodic points for morphisms of PN ⋮ The arithmetic of curves defined by iteration ⋮ Quadratic maps with a periodic critical point of period 2

Cites Work

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• The classification of rational preperiodic points of quadratic polynomials over \(\mathbb{Q}\): A refined conjecture
• Modular curves and the Eisenstein ideal
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• Bounds for the torsion of elliptic curves over number fields
• Rational 6-Cycles Under Iteration of Quadratic Polynomials
• Torsion points on elliptic curves
• Arithmetic properties of periodic points of quadratic maps, II
• Rational Periodic Points of the Quadratic Function Q c (x) = x 2 + c
• Periodic points, multiplicities, and dynamical units.
• ℚ-rational cycles for degree-2 rational maps having an automorphism

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