Orbits of families of vector fields on subcartesian spaces

Jedrzej Śniatycki[1]

  • [1] University of Calgary, Department of Mathematics and Statistics, 2500 University Drive NW, Calgary, Alberta T2N 1N4 (Canada)

Annales de l'Institut Fourier (2003)

  • Volume: 53, Issue: 7, page 2257-2296
  • ISSN: 0373-0956

Abstract

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Orbits of complete families of vector fields on a subcartesian space are shown to be smooth manifolds. This allows a description of the structure of the reduced phase space of a Hamiltonian system in terms of the reduced Poisson algebra. Moreover, one can give a global description of smooth geometric structures on a family of manifolds, which form a singular foliation of a subcartesian space, in terms of objects defined on the corresponding family of vector fields. Stratified spaces, Poisson spaces, and almost complex spaces are discussed as examples.

How to cite

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Śniatycki, Jedrzej. "Orbits of families of vector fields on subcartesian spaces." Annales de l'Institut Fourier 53.7 (2003): 2257-2296. <http://eudml.org/doc/116099>.

@article{Śniatycki2003,
abstract = {Orbits of complete families of vector fields on a subcartesian space are shown to be smooth manifolds. This allows a description of the structure of the reduced phase space of a Hamiltonian system in terms of the reduced Poisson algebra. Moreover, one can give a global description of smooth geometric structures on a family of manifolds, which form a singular foliation of a subcartesian space, in terms of objects defined on the corresponding family of vector fields. Stratified spaces, Poisson spaces, and almost complex spaces are discussed as examples.},
affiliation = {University of Calgary, Department of Mathematics and Statistics, 2500 University Drive NW, Calgary, Alberta T2N 1N4 (Canada)},
author = {Śniatycki, Jedrzej},
journal = {Annales de l'Institut Fourier},
keywords = {almost complex structure; differential spoace; Kähler space; Poisson reduction; singular reduction; stratified space; subcartesian space; differential space},
language = {eng},
number = {7},
pages = {2257-2296},
publisher = {Association des Annales de l'Institut Fourier},
title = {Orbits of families of vector fields on subcartesian spaces},
url = {http://eudml.org/doc/116099},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Śniatycki, Jedrzej
TI - Orbits of families of vector fields on subcartesian spaces
JO - Annales de l'Institut Fourier
PY - 2003
PB - Association des Annales de l'Institut Fourier
VL - 53
IS - 7
SP - 2257
EP - 2296
AB - Orbits of complete families of vector fields on a subcartesian space are shown to be smooth manifolds. This allows a description of the structure of the reduced phase space of a Hamiltonian system in terms of the reduced Poisson algebra. Moreover, one can give a global description of smooth geometric structures on a family of manifolds, which form a singular foliation of a subcartesian space, in terms of objects defined on the corresponding family of vector fields. Stratified spaces, Poisson spaces, and almost complex spaces are discussed as examples.
LA - eng
KW - almost complex structure; differential spoace; Kähler space; Poisson reduction; singular reduction; stratified space; subcartesian space; differential space
UR - http://eudml.org/doc/116099
ER -

References

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