Transitivities of maps on \(G\)-spaces (Q1747866)

In this paper, considering (continuous) self-maps \(f:X\to X\) on a \(G\)-space \(X\), the authors compare properties like, e.g., \(G\)-transitivity, positive \(G\)-transitivity, infinite \(G\)-transitivity of \(f\) via examples and theorems; Section 3 carries a diagram of results. On the other hand in a \(G\)-space \(X\) for a pseudoequivariant map \(f:X\to X\), in Section 4, there are results concerning the interaction of \(G\)-transitivity (resp. positive/infinite \(G\)-transitivity) of \(f:X\to X\) and topological transitivity (resp. positive/infinite topological transitivity) of the induced map on the orbit space \(X/G\).