2008/04/26 by Mauro Patrão, Patrão, Mauro
Mathematics · #22E25 (Secondary) #37A35 #37B40 (Primary) #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #General Topology (math.GN) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.0804.4244
openalex publication_date 2008/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In the present paper, we introduce a natural extension of AKM-topological entropy for noncompact spaces and prove a variational principle which states that the topological entropy, the supremum of the measure theoretical entropies and the minimum of the metric theoretical entropies always coincide. We apply the variational principle to show that the topological entropy of automorphisms of simply connected nilpotent Lie groups always vanishes. This shows that the classical formula for the entropy of an automorphism of a noncompact Lie group is just an upper bound for its topological entropy.