Simplest skew products on \(n\)-dimensional \((n\geq 2 )\) cells, cylinders and tori
The author considers nonwandering sets of \(n\)-dimensional cells, cylinders and tori (for \(n \geq 2\)) and investigates their structure for continuous skew product dynamical systems. The focus is on two particular cases. The first is where the set of periodic points is not empty (for self-maps of tori and cylinders) and closed for all maps. The second is the case where the set of periodic points is empty for self-maps of tori and cylinders and the nonwandering set is minimal. Using previous results found by the author and \textit{E. N. Makhrova} in [Russ. Math. Surv. 76, 821--881 (2021; Zbl 1496.37015)], some generalizations for skew products defined on compact plane rectangles are investigated. The paper includes proofs of the structure results and identification of the trajectories of points under the maps for both cases. In the first case, the maps are periodic; in the second, there is uniform recurrence but not periodicity. As the author notes, the topological entropy for the maps is zero in both cases.
scientific article; zbMATH DE number 7617005
scientific article