Conceptions on topological transitivity in products and symmetric products

Abstract

Having a finite number of topological spaces Xi and functions fi : Xi → Xi , and considering one of the following classes of functions: exact, transitive, strongly transitive, totally transitive, orbit-transitive, strictly orbittransitive, ω -transitive, mixing, weakly mixing, mild mixing, chaotic, exactly Devaney chaotic, minimal, backward minimal, totally minimal, T T++ , scattering, Touhey or an F -system, in this paper, we study dynamical behaviors of the systems (Xi, fi) , ( ∏ Xi, ∏ fi) , (Fn( ∏ Xi), Fn( ∏ fi)) , and (Fn(Xi), Fn(fi)) .