Symplectic singularities and solvable Hamiltonian mappings

• Autorzy: Fukuda T. , Janeczko S.
• Języki publikacji: EN

Abstrakty

EN

We study singularities of smooth mappings (…) of R2n into symplectic space (…) by their isotropic liftings to the corresponding symplectic tangent bundle (…). Using the notion of local solvability of lifting as a generalized Hamiltonian system, we introduce new symplectic invariants and explain their geometric meaning. We prove that a basic local algebra of singularity is a space of generating functions of solvable isotropic mappings over (…) endowed with a natural Poisson structure. The global properties of this Poisson algebra of the singularity among the space of all generating functions of isotropic liftings are investigated. The solvability criterion of generalized Hamiltonian systems is a strong method for various geometric and algebraic investigations in a symplectic space. We illustrate this by explicit classification of solvable systems in codimension one.

Słowa kluczowe

EN

symplectic manifold; Hamiltonian system; solvability; singularities

PL

system Hamiltoniana; rozwiązalność; osobliwości

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2015
• Tom: Vol. 48, nr 2
• Strony: 118--146
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Fukuda T.

• Department of Mathematics, College of Humanities and Sciences, Nihon University, Sakurajousui 3-25-40, Setagaya-Ku, 156-8550 Tokyo, Japan

autor

Janeczko S.

• Institute of Mathematics, Polish Academy of Sciences, Ul. Śniadeckich 8, 00-956 Warsaw, Poland; and Faculty of Mathematics and Information Science, Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, Poland

Bibliografia

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