Geodesic
Orbits connecting singular points in the plane
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 1, pp. 125-132 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

This paper concerns the global structure of planar systems. It is shown that if a positively bounded system with two singular points has no closed orbits, the set of all bounded solutions is compact and simply connected. Also it is shown that for such a system the existence of connecting orbits is tightly related to the behavior of homoclinic orbits. A necessary and sufficient condition for the existence of connecting orbits is given. The number of connecting orbits is also discussed.
This paper concerns the global structure of planar systems. It is shown that if a positively bounded system with two singular points has no closed orbits, the set of all bounded solutions is compact and simply connected. Also it is shown that for such a system the existence of connecting orbits is tightly related to the behavior of homoclinic orbits. A necessary and sufficient condition for the existence of connecting orbits is given. The number of connecting orbits is also discussed.
Classification : 34C11, 34C35, 34C37, 37C29
Keywords: connecting orbit; homoclinic orbit; positively bounded system 
@article{CMJ_2005_55_1_a7,
     author = {Ding, Changming},
     title = {Orbits connecting singular points in the plane},
     journal = {Czechoslovak Mathematical Journal},
     pages = {125--132},
     year = {2005},
     volume = {55},
     number = {1},
     mrnumber = {2121660},
     zbl = {1081.37002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2005_55_1_a7/}
}
TY  - JOUR
AU  - Ding, Changming
TI  - Orbits connecting singular points in the plane
JO  - Czechoslovak Mathematical Journal
PY  - 2005
SP  - 125
EP  - 132
VL  - 55
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/CMJ_2005_55_1_a7/
LA  - en
ID  - CMJ_2005_55_1_a7
ER  - 
%0 Journal Article
%A Ding, Changming
%T Orbits connecting singular points in the plane
%J Czechoslovak Mathematical Journal
%D 2005
%P 125-132
%V 55
%N 1
%U http://geodesic.mathdoc.fr/item/CMJ_2005_55_1_a7/
%G en
%F CMJ_2005_55_1_a7
Ding, Changming. Orbits connecting singular points in the plane. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 1, pp. 125-132. http://geodesic.mathdoc.fr/item/CMJ_2005_55_1_a7/