# On the envelope of a vector field

Banach Center Publications (2011)

- Volume: 94, Issue: 1, page 239-246
- ISSN: 0137-6934

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topBernard Malgrange. "On the envelope of a vector field." Banach Center Publications 94.1 (2011): 239-246. <http://eudml.org/doc/282371>.

@article{BernardMalgrange2011,

abstract = {Given a vector field X on an algebraic variety V over ℂ, I compare the following two objects: (i) the envelope of X, the smallest algebraic pseudogroup over V whose Lie algebra contains X, and (ii) the Galois pseudogroup of the foliation defined by the vector field X + d/dt (restricted to one fibre t = constant). I show that either they are equal, or the second has codimension one in the first.},

author = {Bernard Malgrange},

journal = {Banach Center Publications},

keywords = {vector fields; differential Galois theory},

language = {eng},

number = {1},

pages = {239-246},

title = {On the envelope of a vector field},

url = {http://eudml.org/doc/282371},

volume = {94},

year = {2011},

}

TY - JOUR

AU - Bernard Malgrange

TI - On the envelope of a vector field

JO - Banach Center Publications

PY - 2011

VL - 94

IS - 1

SP - 239

EP - 246

AB - Given a vector field X on an algebraic variety V over ℂ, I compare the following two objects: (i) the envelope of X, the smallest algebraic pseudogroup over V whose Lie algebra contains X, and (ii) the Galois pseudogroup of the foliation defined by the vector field X + d/dt (restricted to one fibre t = constant). I show that either they are equal, or the second has codimension one in the first.

LA - eng

KW - vector fields; differential Galois theory

UR - http://eudml.org/doc/282371

ER -

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