Geodesic
Unbounded Basins of Attraction of Limit Cycles
Acta mathematica Universitatis Comenianae, Tome 72 (2003) no. 1 
P. Giesl. Unbounded Basins of Attraction of Limit Cycles. Acta mathematica Universitatis Comenianae, Tome 72 (2003) no. 1. http://geodesic.mathdoc.fr/item/AMUC_2003_72_1_a7/
@article{AMUC_2003_72_1_a7,
     author = {P. Giesl},
     title = {Unbounded {Basins} of {Attraction} of {Limit} {Cycles}},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2003},
     volume = {72},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2003_72_1_a7/}
}
TY  - JOUR
AU  - P. Giesl
TI  - Unbounded Basins of Attraction of Limit Cycles
JO  - Acta mathematica Universitatis Comenianae
PY  - 2003
VL  - 72
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/AMUC_2003_72_1_a7/
ID  - AMUC_2003_72_1_a7
ER  - 
%0 Journal Article
%A P. Giesl
%T Unbounded Basins of Attraction of Limit Cycles
%J Acta mathematica Universitatis Comenianae
%D 2003
%V 72
%N 1
%U http://geodesic.mathdoc.fr/item/AMUC_2003_72_1_a7/
%F AMUC_2003_72_1_a7

Voir la notice de l'article provenant de la source Comenius University

Consider a dynamical system given by a system of autonomous ordinary differential equations. In this paper we provide a sufficient local condition for an unbounded subset of the phase space to belong to the basin of attraction of a limit cycle. This condition also guarantees the existence and uniqueness of such a limit cycle, if that subset is compact. If the subset is unbounded, the positive orbits of all points of this set either are unbounded or tend to a unique limit cycle.