Reversibility and classification of nilpotent centers (Q1337034)

We consider a germ \(\omega\) of analytic 1-form in \(\mathbb{R}^ 2\), 0 with 1- jet \(ydy\). We prove that if \(\omega= 0\) defines a center (i.e. all solutions are cycles) there exists an analytic involution of \(\mathbb{R}^ 2\), 0 preserving the phase portrait of the system. Geometrically this means that analytic nilpotent centers are built by pull back with fold applications. A theorem of equivariant conjugacy leads to the complete classification of such centers.