On implicit Lagrangian differential systems

S. Janeczko

Annales Polonici Mathematici (2000)

  • Volume: 74, Issue: 1, page 133-141
  • ISSN: 0066-2216

Abstract

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Let (P,ω) be a symplectic manifold. We find an integrability condition for an implicit differential system D' which is formed by a Lagrangian submanifold in the canonical symplectic tangent bundle (TP,ὡ).

How to cite

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Janeczko, S.. "On implicit Lagrangian differential systems." Annales Polonici Mathematici 74.1 (2000): 133-141. <http://eudml.org/doc/208361>.

@article{Janeczko2000,
abstract = {Let (P,ω) be a symplectic manifold. We find an integrability condition for an implicit differential system D' which is formed by a Lagrangian submanifold in the canonical symplectic tangent bundle (TP,ὡ).},
author = {Janeczko, S.},
journal = {Annales Polonici Mathematici},
keywords = {implicit differential equation; symplectic manifold; integrability; Lagrangian manifold; integrable system},
language = {eng},
number = {1},
pages = {133-141},
title = {On implicit Lagrangian differential systems},
url = {http://eudml.org/doc/208361},
volume = {74},
year = {2000},
}

TY - JOUR
AU - Janeczko, S.
TI - On implicit Lagrangian differential systems
JO - Annales Polonici Mathematici
PY - 2000
VL - 74
IS - 1
SP - 133
EP - 141
AB - Let (P,ω) be a symplectic manifold. We find an integrability condition for an implicit differential system D' which is formed by a Lagrangian submanifold in the canonical symplectic tangent bundle (TP,ὡ).
LA - eng
KW - implicit differential equation; symplectic manifold; integrability; Lagrangian manifold; integrable system
UR - http://eudml.org/doc/208361
ER -

References

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  3. [3] I. Ekeland, Discontinuités de champs hamiltoniens et existence de solutions optimales en calcul des variations, Publ. Math. I.H.E.S. 47 (1977), 5-32. Zbl0447.49015
  4. [4] S. Janeczko, Systems of rays in the presence of distribution of hyperplanes, in: Banach Center Publ. 32, Inst. Math., Polish Acad. Sci., 1995, 245-260. Zbl0844.57030
  5. [5] S. Janeczko, Hamiltonian geodesics in nonholonomic differential systems, Reports Math. Phys. 40 (1997), 217-224. Zbl0911.58003
  6. [6] S. Janeczko, On isotropic submanifolds and evolution of quasicaustics, Pacific J. Math. 158 (1993), 317-334. Zbl0806.58023
  7. [7] J. Kijowski and W. M. Tulczyjew, A Symplectic Framework for Field Theories, Lecture Notes in Physics 107, Springer, 1979. Zbl0439.58002
  8. [8] J. Martinet, Singularities of Smooth Functions and Maps, Cambridge Univ. Press, Cambridge, 1982. 
  9. [9] J. N. Mather, Solutions of generic linear equations, in: Dynamical Systems (Salvador, 1971), Academic Press, 1973, 185-193. 
  10. [10] R. Montgomery, A survey of singular curves in sub-Riemannian geometry, J. Dynam. Control Systems 1 (1995), 49-90. Zbl0941.53021
  11. [11] J. Śniatycki and W. M. Tulczyjew, Generating forms of Lagrangian submanifolds, Indiana Univ. Math. J. 22 (1972), 267-275. Zbl0237.58002
  12. [12] F. Takens, Implicit differential equations: some open problems, in: Lecture Notes in Math. 535, Springer, 1976, 237-253. 
  13. [13] R. Thom, Sur les équations différentielles multiformes et leurs intégrales singulières, Bol. Soc. Brasil. Mat. 3 (1972), 1-11. Zbl0396.34018
  14. [14] A. Weinstein, Lectures on Symplectic Manifolds, CBMS Regional Conf. Ser. in Math. 29, Amer. Math. Soc., Providence, RI, 1977. 

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