On some strong chaotic properties of dynamical systems

Some Chaotic Results of Product on Zero Dimension Spaces

“…In another work [3], Dzul-kifli and Good showed that the set of points with prime period at least is dense for each if is Devaney chaotic on a compact metric space with no isolated points . In their article [4], Baloush and Dzul-kifli introduced six various one-step shifts of finite types, with totally different dynamic demeanor, and clearified the dynamics of each space Other authors [5] showed that the expression "Locally Everywhere Onto" implies many other chaos properties such as mixing, totally transitive ,and blending. Another study investigated how chaos conditions on maps hold over to their products [6].…”

Some Chaos Notions on Dendrites

“…x is periodic point of period greater than or equal to m} is dense. The works in [6][7][8][9][10][11] discussed the relation between strong dense periodicity and other notions of chaos on intervals, circles and shift of finite space.…”

“…According to [5], a strongly blending map on a subset A ⊆ R n , whose set of periodic points is dense, implies transitivity. Moreover, on compact space, locally everywhere onto implies strongly blending [10], while mixing is sufficient to imply weakly blending [6]. On the other hand, Banks and Trotta [13] proved that weakly mixing implies strongly blending on the graph.…”