Geodesic
A criterion for completeness of an~analytic vector field on a~locally compact Abelian group
Sbornik. Mathematics, Tome 83 (1995) no. 2, pp. 297-313

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We give a criterion for completeness of a compactly supported analytic vector field $C$ on a locally compact Abelian group $X$. It is shown that $C$ gives rise to an analytic flow in $X$ if and only if there exists on $X$ a fundamental family of cylindrical differential systems (Frobenius distributions) that are stable with respect to the action of $C$. 
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     author = {S. S. Akbarov},
     title = {A criterion for completeness of an~analytic vector field on a~locally compact {Abelian} group},
     journal = {Sbornik. Mathematics},
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     volume = {83},
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     year = {1995},
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S. S. Akbarov. A criterion for completeness of an~analytic vector field on a~locally compact Abelian group. Sbornik. Mathematics, Tome 83 (1995) no. 2, pp. 297-313. http://geodesic.mathdoc.fr/item/SM_1995_83_2_a0/