Methods and Applications of Analysis
Volume 25 (2018)
In Memory of Professor John N. Mather: Part 1 of 3
Guest Editors: Sen Hu, University of Science and Technology, China; Stanisław Janeczko, Polish Academy of Sciences, Poland; Stephen S.-T. Yau, Tsinghua University, China; and Huaiqing Zuo, Tsinghua University, China.
Solvable submanifolds of tangent bundle and J. Mather generic linear equations
Pages: 233 – 256
Using J. Mather results on solutions of generic linear equations the smooth solvability of implicit differential systems is investigated. Implicit Hamiltonian systems are considered and algebraic version of J. Mather theorem was applied in this case. For the generalized Hamiltonian systems defined by P.A.M. Dirac on smooth constraints we find the corresponding Poisson–Lie algebras as a basic symplectic invariants of submanifolds in the symplectic space.
symplectic manifold, singularities, Hamiltonian systems, Poisson–Lie algebras
2010 Mathematics Subject Classification
Received 15 July 2018
Accepted 29 January 2019
Published 1 November 2019