HEIGHT BOUND AND PREPERIODIC POINTS FOR JOINTLY REGULAR FAMILIES OF RATIONAL MAPS

DOI10.4134/JKMS.2011.48.6.1171zbMath1260.37066arXiv1003.3241OpenAlexW2963061408MaRDI QIDQ3098019

Chong Gyu Lee

Publication date: 11 November 2011

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

Abstract: Silverman proved a height inequality for jointly regular family of rational maps and the author improved it for jointly regular pairs. In this paper, we provide the same improvement for jointly regular family; if S is a jointly regular set of rational maps, then sum_{fin S} dfrac{1}{deg f} h�igl(f(P) �igr) > (1+ dfrac{1}{r}) f(P) - C where r = max_{fin S} r(f).

Full work available at URL: https://arxiv.org/abs/1003.3241

zbMATH Keywords

heightrational mappreperiodic pointsjointly regular family

Mathematics Subject Classification ID

Heights (11G50) Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables (32H50) 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)

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