Geodesic
Orbits connecting singular points in the plane
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 1, pp. 125-132
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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 
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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/

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