On singularities of Hamiltonian mappings

Volume 82 / 2008

Takuo Fukuda, Stanisław Janeczko Banach Center Publications 82 (2008), 55-69 MSC: 37J35, 57R45, 58C35, 70H05. DOI: 10.4064/bc82-0-4


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.


  • Takuo FukudaDepartment of Mathematics
    College of Humanities and Sciences
    Nihon University
    3-25-40 Sakurajousui, Setagaya-ku
    Tokyo, Japan
  • Stanisław JaneczkoInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-956 Warszawa, Poland,
    Faculty of Mathematics and Information Science
    Warsaw University of Technology
    Plac Politechniki 1
    00-661 Warszawa, Poland

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