  We study nonlinear automorphisms of Levi degenerate hypersurfaces of finite
multitype. By recent results of Kolar, Meylan and Zaitsev, the Lie algebra of
infinitesimal CR automorphisms may contain a graded component consisting of
nonlinear vector fields of arbitrarily high degree, which has no analog in the
classical Levi nondegenerate case, or in the case of finite type hypersurfaces
in $\mathbb C^2$. We analyze this phenomenon for hypersurfaces of finite Catlin
multitype in complex dimension three. The results provide a complete
classification of such manifolds. As a consequence, we show on which
hypersurfaces 2-jets are not sufficient to determine an automorphism. The
results also confirm a conjecture about the origin of nonlinear automorphisms
of Levi degenerate hypersurfaces, formulated by the first author (AIM 2010).
