Pisot units, Salem numbers, and higher dimensional projective manifolds with primitive automorphisms of positive entropy. (English) Zbl 1432.37010
Summary: We show that, in any dimension greater than one, there are an abelian variety, a smooth rational variety and a Calabi-Yau manifold, with primitive birational automorphisms of first dynamical degree \(>1\). We also show that there are smooth complex projective Calabi-Yau manifolds and smooth rational manifolds, of any even dimension, with primitive biregular automorphisms of positive topological entropy.
MSC:
37A44 | Relations between ergodic theory and number theory |
37P55 | Arithmetic dynamics on general algebraic varieties |
14J32 | Calabi-Yau manifolds (algebro-geometric aspects) |
14H37 | Automorphisms of curves |
14J50 | Automorphisms of surfaces and higher-dimensional varieties |