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.
@article{bwmeta1.element.bwnjournal-article-apmv58z1p19bwm, author = {Andrzej Zajtz}, title = {Some division theorems for vector fields}, journal = {Annales Polonici Mathematici}, volume = {58}, year = {1993}, pages = {19-28}, zbl = {0779.17022}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv58z1p19bwm} }
Andrzej Zajtz. Some division theorems for vector fields. Annales Polonici Mathematici, Tome 58 (1993) pp. 19-28. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv58z1p19bwm/
[000] [1] E. Nelson, Topics in Dynamics, I. Flows, Princeton University Press, Princeton 1969. | Zbl 0197.10702
[001] [2] S. Sternberg, On the structure of local homeomorphisms of Euclidean n-space, II, Amer. J. Math. 80 (1958), 623-631. | Zbl 0083.31406