Forcing relations for homoclinic orbits of the Smale horseshoe map.
Collins, Pieter (2005)
Experimental Mathematics
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Forcing relations for homoclinic orbits of the Smale horseshoe map.
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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. ...