2020/01/31 by Lucas Dahinden · 1 citation
Mathematics · #math.SG #math.DS #msc:53D35 #msc:53D40 #msc:37B40 #msc:57R17 #msc:55N31
paper · pdf · doi:10.1142/s0219199721500152
arxiv created 2021/02/10 · arxiv updated 2021/02/11
Topological entropy is not lower semi-continous: small perturbation of the dynamical system can lead to a collapse of entropy. In this note we show that for some special classes of dynamical systems (geodesic flows, Reeb flows, positive contactomorphisms) topological entropy at least is stable in the sense that there exists a nontrivial continuous lower bound, given that a certain homological invariant grows exponentially.