COUNTEREXAMPLES IN CHAOTIC GENERALIZED SHIFTS

In the following text for arbitrary X with at least two elements, nonempty countable set Г we make a comparative study on the collection of generalized shift dynamical systems like (X^Г,σφ) where φ : Г → Г is an arbitrary self-map. We pay attention to sub-systems and combinations of generalized shifts with counter examples regarding Devaney, exact Devaney, Li-Yorke, e-chaoticity and P-chaoticity.