ON THE NUMBER OF RATIONAL ITERATED PREIMAGES OF THE ORIGIN UNDER QUADRATIC DYNAMICAL SYSTEMS

DOI10.1142/S1793042111004162zbMath1242.14019arXiv0810.1715OpenAlexW2964254030MaRDI QIDQ3101581

Michael Stoll, Xander Faber, Benjamin Hutz

Publication date: 29 November 2011

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0810.1715

zbMATH Keywords

rational pointsarithmetic geometryquadratic dynamical systems

Mathematics Subject Classification ID

Rational points (14G05) Computer solution of Diophantine equations (11Y50) Arithmetic aspects of modular and Shimura varieties (11G18) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10)

Related Items (3)

Dynamics of quadratic polynomials and rational points on a curve of genus 4 ⋮ Rational preimages in families of dynamical systems ⋮ A remark on the effective Mordell conjecture and rational pre-images under quadratic dynamical systems

Uses Software

• Magma

Cites Work

• Height difference bounds for elliptic curves over number fields
• Twists of \(X(7)\) and primitive solutions to \(x^2+y^3=z^7\)
• \(K3\) surfaces with Picard number one and infinitely many rational points
• Uniform bounds on pre-images under quadratic dynamical systems
• The classification of rational preperiodic points of quadratic polynomials over \(\mathbb{Q}\): A refined conjecture
• Modular curves and the Eisenstein ideal
• The Magma algebra system. I: The user language
• Cycles of quadratic polynomials and rational points on a genus-2 curve
• Implementing 2-descent for Jacobians of hyperelliptic curves
• Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians of genus 2 curves
• Rational 6-Cycles Under Iteration of Quadratic Polynomials
• The Mordell–Weil sieve: proving non-existence of rational points on curves
• On the height constant for curves of genus two, II
• Computing Special Values of MotivicL-Functions
• Independence of rational points on twists of a given curve

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