On the preperiodic points of an endomorphism of ℙ¹×ℙ¹ which lie on a curve

DOI10.1090/S0002-9947-2012-05557-7zbMath1300.14029OpenAlexW1549586061MaRDI QIDQ4915333

Arman Mimar

Publication date: 10 April 2013

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

Full work available at URL: https://doi.org/10.1090/s0002-9947-2012-05557-7

zbMATH Keywords

Julia setspreperiodic pointscapacity theorydynamical Manin-MumfordZhang's height

Mathematics Subject Classification ID

Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) 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 ⋮ Height coincidences in products of the projective line ⋮ Preperiodic points and unlikely intersections ⋮ A dynamical pairing between two rational maps ⋮ The arithmetic Hodge index theorem and rigidity of dynamical systems over function fields ⋮ Proof of a dynamical Bogomolov conjecture for lines under polynomial actions ⋮ The arithmetic Hodge index theorem for adelic line bundles ⋮ The dynamical Manin–Mumford conjecture and the dynamical Bogomolov conjecture for endomorphisms of ⋮ ABC implies there are infinitely many non-Fibonacci-Wieferich primes

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