Standard decomposition of expansive ergodically supported dynamics

摘要

In this work, we introduce the notion of weak quasigroups, which are quasigroup operations defined almost everywhere on some set.Then, we prove that the topological entropy and the ergodic period of an invertible expansive ergodically supported dynamical system (X, T) with the shadowing property establish a sufficient criterion for the existence of quasigroup operations defined almost everywhere outside of universally null sets and for which T is an automorphism. Furthermore, we find a decomposition of the dynamics of T in terms of T -invariant weak topological subquasigroups.