On singularities of Hamiltonian mappings
Volume 82 / 2008
Banach Center Publications 82 (2008), 55-69
MSC: 37J35, 57R45, 58C35, 70H05.
DOI: 10.4064/bc82-0-4
Abstract
The notion of an implicit Hamiltonian system—an isotropic mapping $H:M\to (TM,\dot\omega )$ into the tangent bundle endowed with the symplectic structure defined by canonical morphism between tangent and cotangent bundles of $M$—is studied. The corank one singularities of such systems are classified. Their transversality conditions in the 1-jet space of isotropic mappings are described and the corresponding symplectically invariant algebras of Hamiltonian generating functions are calculated.
