Stability is not open (Q717805)

A closed hypersurface \(\Sigma\) in a symplectic manifold \((M,\Omega)\) is called stable if a neighbourhood of \(\Sigma\) can be foliated by hypersurfaces whose characteristic folitions are conjugate; the characteristic foliation on a hypersurface \(\Sigma\) being defined by the one-dimensional distribution \(\ker(\Omega/\Sigma)\). The authors establish the following theorem: There exist a stable closed hypersurface \(\Sigma\) in a symplectic 6-manifold, and a neighbourhood of \(\Sigma\) in the space of closed hypersurfaces which contains an open dense set consisting of unstable hypersurfaces.