Answering two open problems on Banks theorem for non-autonomous dynamical systems

Abstract

This paper shows that (1) there exists a topologically transitive NADS having two disjoint invariant periodic orbits with dense periodic points, which is finitely generated but not periodic; (2) there exists a topologically transitive non-finitely generated NADS having two disjoint invariant periodic orbits with dense periodic point, which is not sensitive. This answers positively the Open Problems 4.1 and 4.2 posed in [8].