Dynamical degrees of automorphisms on abelian varieties

2020/07/03 by Nguyen-Bac Dang, Dang, Nguyen-Bac, Thorsten Herrig +1 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Mathematical Dynamics and Fractals #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2007.01914

Abstract

For any given Salem number, we construct an automorphism on a simple abelian variety whose first dynamical degree is the square of the Salem number. Our construction works for both simple abelian varieties with totally indefinite quaternion multiplication and for simple abelian varieties of the second kind. We then give a complete classification of the dynamical degree sequences for abelian varieties of dimension at most four and obtain an ergodic result for sequences of pullbacks of forms.

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