A dynamical pairing between two rational maps

DOI10.1090/S0002-9947-2011-05350-XzbMath1300.37052arXiv0911.1875MaRDI QIDQ5389408

Lucien Szpiro, Thomas J. Tucker, Clayton Petsche

Publication date: 26 April 2012

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0911.1875

zbMATH Keywords

arithmetic dynamical systemscanonical heightsequidistribution of small points

Mathematics Subject Classification ID

Heights (11G50) Arithmetic varieties and schemes; Arakelov theory; heights (14G40) Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps (37P05) Height functions; Green functions; invariant measures in arithmetic and non-Archimedean dynamical systems (37P30)

Related Items (9)

Greatest common divisors of iterates of polynomials ⋮ Mahler measure of polynomial iterates ⋮ A dynamical construction of small totally \(p\)-adic algebraic numbers ⋮ Abelian extensions in dynamical Galois theory ⋮ Height bounds for algebraic numbers satisfying splitting conditions ⋮ On the preperiodic points of an endomorphism of ℙ¹×ℙ¹ which lie on a curve ⋮ Common preperiodic points for quadratic polynomials ⋮ The Arakelov-Zhang pairing and Julia sets ⋮ Integral division points on curves

Cites Work

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• Preperiodic points and unlikely intersections
• Calculus on arithmetic surfaces
• Equidistribution of small points
• Limit distribution of small points on algebraic tori
• Equidistribution of small points, rational dynamics, and potential theory
• Mahler measures and logarithmic equidistribution
• Invariant sets under iteration of rational functions
• Quantitative uniform distribution of points of small height on the projective line
• Equidistribution and generalized Mahler measures
• An invariant measure for rational maps
• Speculations Concerning the Range of Mahler's Measure
• Heights of Projective Varieties and Positive Green Forms
• On the preperiodic points of an endomorphism of ℙ¹×ℙ¹ which lie on a curve
• Dynamics of projective morphisms having identical canonical heights
• Mesures et équidistribution sur les espaces de Berkovich
• Dynamics in One Complex Variable. (AM-160)
• Théorie ergodique des fractions rationnelles sur un corps ultramétrique

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