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.
Classification : 34C11, 34C35, 34C37, 37C29
Keywords: connecting orbit; homoclinic orbit; positively bounded system 
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     author = {Ding, Changming},
     title = {Orbits connecting singular points in the plane},
     journal = {Czechoslovak Mathematical Journal},
     pages = {125--132},
     publisher = {mathdoc},
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     year = {2005},
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     zbl = {1081.37002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2005__55_1_a7/}
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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/