Canonical Heights and Monomial Maps: On Effective Lower Bounds for Points with Dense Orbit

TL;DR

This paper establishes effective lower bounds for the canonical heights of points with Zariski dense orbits under monomial maps, specifically for cases where the endomorphisms are induced by matrices with real Jordan form, advancing understanding of dynamical heights.

Contribution

It provides the first effective lower bounds for canonical heights in monomial dynamical systems with matrices in real Jordan form, extending previous theoretical results.

Findings

Effective lower bounds for heights of points with dense orbits

Applicable to monomial maps with matrices in real Jordan form

Advances in understanding dynamical heights in algebraic dynamics

Abstract

We prove, for the canonical height defined by Silverman [15] 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.