# Some division theorems for vector fields

Annales Polonici Mathematici (1993)

- Volume: 58, Issue: 1, page 19-28
- ISSN: 0066-2216

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topAndrzej Zajtz. "Some division theorems for vector fields." Annales Polonici Mathematici 58.1 (1993): 19-28. <http://eudml.org/doc/262287>.

@article{AndrzejZajtz1993,

abstract = {This paper is concerned with the problem of divisibility of vector fields with respect to the Lie bracket [X,Y]. We deal with the local divisibility. The methods used are based on various estimates, in particular those concerning prolongations of dynamical systems. A generalization to polynomials of the adjoint operator (X) is given.},

author = {Andrzej Zajtz},

journal = {Annales Polonici Mathematici},

keywords = {Lie bracket of vector fields; bounds to flow and its prolongations; Lie bracket of vector field; divisibility; homogeneous vector fields; prolongations of dynamical systems},

language = {eng},

number = {1},

pages = {19-28},

title = {Some division theorems for vector fields},

url = {http://eudml.org/doc/262287},

volume = {58},

year = {1993},

}

TY - JOUR

AU - Andrzej Zajtz

TI - Some division theorems for vector fields

JO - Annales Polonici Mathematici

PY - 1993

VL - 58

IS - 1

SP - 19

EP - 28

AB - This paper is concerned with the problem of divisibility of vector fields with respect to the Lie bracket [X,Y]. We deal with the local divisibility. The methods used are based on various estimates, in particular those concerning prolongations of dynamical systems. A generalization to polynomials of the adjoint operator (X) is given.

LA - eng

KW - Lie bracket of vector fields; bounds to flow and its prolongations; Lie bracket of vector field; divisibility; homogeneous vector fields; prolongations of dynamical systems

UR - http://eudml.org/doc/262287

ER -

## References

top- [1] E. Nelson, Topics in Dynamics, I. Flows, Princeton University Press, Princeton 1969. Zbl0197.10702
- [2] S. Sternberg, On the structure of local homeomorphisms of Euclidean n-space, II, Amer. J. Math. 80 (1958), 623-631. Zbl0083.31406

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