Existence and partial characterization of the global attractor for the sunflower equation (Q1892516)

Consider the sunflower equation \((*)\) \(\varepsilon x'' + ax'(t) + b \sin x (t -\varepsilon) = 0\) as retarded functional differential equation on the cylinder \(S^1 \times R\). The author proves: (i) For \(\varepsilon \geq 0\), \((*)\) has a connected global attractor \(S_\varepsilon\) which is upper semicontinuous in \(\varepsilon\). (ii) For \(\varepsilon \in [0, {a \over b}]\), \(S_\varepsilon\) is homeomorphic to \(S^1\).