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

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 points, which is not sensitive. This answers positively the Open Problems 4.1 and 4.2 posed in Yang and Li [A remark on Banks theorem, J. Difference Equ. Appl. 24 (2018), pp. 1777–1782].