# Publishing house / Banach Center Publications / All volumes

## 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.

#### Authors

College of Humanities and Sciences
Nihon University
3-25-40 Sakurajousui, Setagaya-ku
Tokyo, Japan
• Stanisław JaneczkoInstitute of Mathematics
00-956 Warszawa, Poland,
and
Faculty of Mathematics and Information Science
Warsaw University of Technology
Plac Politechniki 1
00-661 Warszawa, Poland
e-mail

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