Methods and Applications of Analysis

Volume 25 (2018)

Number 3

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

DOI: https://dx.doi.org/10.4310/MAA.2018.v25.n3.a4

Authors

Takuo Fukuda (Department of Mathematics College of Humanities and Sciences, Nihon University, Setagaya-ku, Tokyo, Japan)

Stanisław Janeczko (Instytut Matematyczny PAN, Warszawa, Poland; and Wydzial Matematyki i Nauk Informacyjnych, Politechnika Warszawska, Poland)

Abstract

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.

Keywords

symplectic manifold, singularities, Hamiltonian systems, Poisson–Lie algebras

2010 Mathematics Subject Classification

37J05, 57R45

Full Text (PDF format)

Received 15 July 2018

Accepted 29 January 2019

Published 1 November 2019