14.15-15.10, rum 3721, Richard Miles (KTH): Dirichlet series for finite combinatorial rank dynamics

Abstract. This talk will concern the orbit counting problem for algebraic dynamical systems. I will review some facts concerning periodic point counting and discuss a class of group endomorphisms exhibiting slow orbit growth. An associated dynamical Dirichlet series is found to have a convenient closed rational form and analytic properties of the Dirichlet series are related to orbit growth asymptotics; depending on the location of the abscissa of convergence and the degree of the pole there, various orbit-growth asymptotics are found, all of which are polynomially bounded.