Equivariant normal form for nondegenerate singular orbits pairs of restricted integrable Hamiltonian systems pairs on contact pairs.

Abstract

On a differential manifold (M2h+2k+2, η, α) equipped to contact pair, we introduce the notion of
restricted completely integrable Hamiltonian system pair with (k +h) degrees of freedom whose first
integrals are invariant under the contact action of a compact Lie group G. We show that the singular
Legendrian foliation pair associated to this restricted completely integrable Hamiltonian system is
contact equivalent, in a G-equivariant way, to the linearised foliation pair in a neighbourhood of a
nondegenerate singular compact orbit pair.