Some types of topological transitivity and the relationships between them in dynamical systems

This thesis consists of four main sections. In the first section, the concepts used throughout the thesis are defined, some features are mentioned, and the chaotic behaviors of shift maps are examined. In the second section of the thesis, situations indicating topological transitivity and the implications of these situations are addressed. Also, the equivalent concepts of topological transitivity and the relationship between topological transitivity and weak transitivity have been examined. In the third section of the thesis, counterexamples are provided for the situations examined in the previous section. In the last section of the thesis, one-sided shift map have been examined in product spaces, and maps with different chaotic properties have been constructed in the sequence spaces covered within the scope of the thesis.