We give a necessary and sufficient condition for local controllability around closed orbits for general smooth control systems. We also prove that any such system on a compact manifold has a closed orbit.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba62-1-8, author = {Marek Grochowski}, title = {Local Controllability around Closed Orbits}, journal = {Bulletin of the Polish Academy of Sciences. Mathematics}, volume = {62}, year = {2014}, pages = {77-85}, zbl = {1298.93183}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba62-1-8} }
Marek Grochowski. Local Controllability around Closed Orbits. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 62 (2014) pp. 77-85. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba62-1-8/