Newton's method over global height fields

DOI10.5802/jtnb.870zbMath1392.37101arXiv1212.6409OpenAlexW2963093012MaRDI QIDQ2341680

Adam Towsley, Xander Faber

Publication date: 27 April 2015

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.6409

zbMATH Keywords

Newton's methodarithmetic dynamicsglobal height field

Mathematics Subject Classification ID

Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps (37P05) Dynamical systems over global ground fields (37P15)

Cites Work

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• On the number of places of convergence for Newton's method over number fields
• Families of rational maps and convergence basins of Newton's method
• Periods of rational maps modulo primes
• A HASSE PRINCIPLE FOR PERIODIC POINTS
• Prime factors of dynamical sequences
• A finiteness theorem for canonical heights attached to rational maps over function fields
• A local-global criterion for dynamics on P¹

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