Symplectic Singularities and Solvable Hamiltonian Mappings

Demonstratio mathematica

article

Takuo Fukuda¹  Stanislaw Janeczko² 

[1] DEPARTMENT OF MATHEMATICS COLLEGE OF HUMANITIES AND SCIENCES NIHON UNIVERSITY SAKURAJOUSUI 3-25-40;INSTITUTE OF MATHEMATICS POLISH ACADEMY OF SCIENCES;FACULTY OF MATHEMATICS AND INFORMATION SCIENCE WARSAW UNIVERSITY OF TECHNOLOGY Koszykowa 75 00-662 WARSAW

关键词: symplectic manifold;    Hamiltonian system;    solvability;    singularities.;   

DOI  :  10.1515/dema-2015-0014

学科分类：外科医学

来源: De Gruyter

【 摘 要 】

We study singularities of smooth mappings F̄ of ℝ 2n into symplectic space (ℝ 2n , ω̇) by their isotropic liftings to the corresponding symplectic tangent bundle (Tℝ 2n ,w). 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 F̄ 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.

【 授权许可】

CC BY