[Author]
 Kalnitsky V. S.

[Title]
 Symmetries of weak-controllable systems

[AMS Subj-class]
 53C22 Geodesics

[Keywords]
 spray, symmetry, controllable system, completeness

[Abstract]
 Weak-controllability is the extension of the notions
 used in Nonlinear Control System Theory. This notion turned out to
 be applicable to the question of completeness of the affine
 connection spray symmetry. The main result can be considered as an
 extension of old Kobayashi theorem which ascertains the
 completeness of the Jacobi fields provided the spray is complete.
 In this article we formulate also sufficient conditions for
 completeness of the spray itself.

[Comments]
 LaTeX, English, 6 pp.
 Submited to journal: Symmetry, Integrability and Geometry: Methods and Applications.

[Contact e-mail]
 skalnitsky@hotmail.com