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arXiv · 1003.3241

Height bound and preperiodic points for jointly regular families of rational maps

ChongGyu Lee
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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_{f\in S} \dfrac{1}{°f} h\bigl(f(P) \bigr) > (1+ \dfrac{1}{r}) f(P) - C where r = \max_{f\in S} r(f).

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ChongGyu Lee. 2010-04-26. Height bound and preperiodic points for jointly regular families of rational maps. https://arxiv.org/abs/1003.3241

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