Let M^m be a compact m-manifold and \varphi: R^n × M^m \rightarrow M^m a C^r, r \geq 1, action with infinitesimal generators of class C^r . We introduce the concept of transversally hyperbolic singular orbit for an action \varphi and explore this concept in its relations to stability. Our main result says that if m = n and O_p is a compact singular orbit of \varphi that is transversally hyperbolic, then \varphi is C^1 locally structurally stable at O_p.
@article{7435,
title = {Local structural stability of actions of R^n on n-manifolds - doi: 10.5269/bspm.v24i1-2.7435},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {23},
year = {2009},
doi = {10.5269/bspm.v24i1-2.7435},
language = {EN},
url = {http://dml.mathdoc.fr/item/7435}
}
Maquera, Carlos; Arraut, J. L. Local structural stability of actions of R^n on n-manifolds - doi: 10.5269/bspm.v24i1-2.7435. Boletim da Sociedade Paranaense de Matemática, Tome 23 (2009) . doi : 10.5269/bspm.v24i1-2.7435. http://gdmltest.u-ga.fr/item/7435/