Étale dynamical systems and topological entropy

Abstract

Abstract. In this paper, we consider two questions about topological entropy of dynamical systems. We propose to resolve these questions by the same approach of usinǵ etale analogs of topological and algebraic dynamical systems.The first question is to define topological entropy for a topological dynamical system (f, X, Ω). The main idea is to make use -in addition to invariant compact subspaces of (X, Ω) -of compactifications ofétale covers• π and the fibers of π are all finite. We prove some basic results and propose a conjecture, whose validity allows us to prove further results.The second question is to define topological entropy for algebraic dynamical systems,with the requirement that it should be as close to the pullback on cohomology groups as possible. To this end, we develop anétale analog of algebraic dynamical systems.

Some interesting birational morphisms of smooth affine quadric 3-folds *

“…It is interesting to see whether the ideas in [20] work for our map f c (or F). One can also try to check if the more general approach of using etale covers of the map (but then, must work with correspondences in general) in [60] can work.…”