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 thefollowing 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, backwardminimal, totally minimal, T T++ , scattering, Touhey or an F -system, in this paper, we study dynamical behaviors ofthe systems (Xi, fi), (∏Xi,∏fi), (Fn(∏Xi), Fn(∏fi)), and (Fn(Xi), Fn(fi)).