Accumulation points of flows on the Klein bottle (Q1865972)

The paper characterizes the sets that can occur as omega-limit sets of smooth flows on the Klein bottle \(K\), by defining a notion of admissible set and showing that any omega-limit set is the boundary of an admissible set, and conversely, given an admissible set \(S\subset K\) there is a smooth flow on \(K\) and a point \(x\) of \(S\) such that the omega-limit set of \(x\) is the boundary of \(S\). \(S\subset K\) is admissible provided that it is a proper, connected, open subset whose complement is connected, and with the property that for any non null homotopic Jordan curve \(\beta\) in \(S\), \ there is a component \(C\) of \(S - \beta\) such that the boundary of \(C\) contains that of \(S\).