Agrachev, A. A.; Gamkrelidze, R. V. On the orbits of groups of diffeomorphisms and flows. (English. Russian original) Zbl 0902.58004 Proc. Steklov Inst. Math. 209, 1-10 (1995); translation from Tr. Mat. Inst. Steklova 209, 3-13 (1995). Let \(M\) be a real-analytic manifold, \(\text{Diff}(M)\) the group of analytic diffeomorphisms, \(\text{Vect}(M)\) the Lie algebra of analytic vector fields. The Nagano-Sussmann theorem says that the orbits of a subgroup \(G\) of \(\text{Diff}(M)\), which is generated by its one-parameter subgroups, are immersed analytic submanifolds [see T. Nagano, J. Math. Soc. Japan 18, 398-404 (1966; Zbl 0147.23502) and H. J. Sussmann, Trans. Am. Math. Soc. 180, 171-188 (1973; Zbl 0274.58002)]. Here it is shown that it suffices to assume that points in \(G\) can be connected by piecewise-analytic curves in \(G\) instead of one-parameter subgroups.For the entire collection see [Zbl 0863.00018]. Reviewer: A.Kriegl (Wien) Cited in 1 Document MSC: 58D05 Groups of diffeomorphisms and homeomorphisms as manifolds Keywords:group of analytic diffeomorphisms; analytic vector fields; orbits of a subgroup Citations:Zbl 0147.23502; Zbl 0274.58002 PDFBibTeX XMLCite \textit{A. A. Agrachev} and \textit{R. V. Gamkrelidze}, in: Singularities of smooth mappings with additional structures. Collected papers. Moscow: Maik Nauka/Interperiodica Publishing. 1 (1995; Zbl 0902.58004); translation from Tr. Mat. Inst. Steklova 209, 3--13 (1995)