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/