Manfred Einsiedler

Amoebas and algebraic dynamic

I will describe how amoebas help to describe the dynamical properties of $\mathbb Z^d$-actions by automorphisms of compact abelian groups, and give concrete examples for that connection. One property, that is best characterized by the amoeba, is expansiveness of subactions. A $\mathbb Z^k$-subaction is expansive if there exists an $\epsilon>0$ such that there are not two points $x\neq y$ that stay $\epsilon$-close forever (for the $\mathbb Z^k$-action).