The notion of an implicit Hamiltonian system-an isotropic mapping H: M → (TM,ω̇) 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc82-0-4,
author = {Takuo Fukuda and Stanis\l aw Janeczko},
title = {On singularities of Hamiltonian mappings},
journal = {Banach Center Publications},
volume = {83},
year = {2008},
pages = {55-69},
zbl = {1153.37401},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc82-0-4}
}
Takuo Fukuda; Stanisław Janeczko. On singularities of Hamiltonian mappings. Banach Center Publications, Tome 83 (2008) pp. 55-69. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc82-0-4/