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Canonical heights and monomial maps: on effective lower bounds for points with dense orbit. (English) Zbl 1436.37102

Summary: We prove, for the canonical height defined by J. H. Silverman [Ergodic Theory Dyn. Syst. 34, No. 2, 647–678 (2014; Zbl 1372.37093)] on monomial maps, the existence of effective lower bounds for heights of points with Zariski dense orbit, for cases with endomorphisms induced by matrices with real Jordan form.

MSC:

37P30 Height functions; Green functions; invariant measures in arithmetic and non-Archimedean dynamical systems
37P55 Arithmetic dynamics on general algebraic varieties
11G50 Heights
14E05 Rational and birational maps

Citations:

Zbl 1372.37093
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References:

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