Orbits connecting singular points in the plane |
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| Authors: | Changming Ding |
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| Institution: | (1) Department of Applied Mathematics, Zhejiang University of Technology, 310032 Hangzhou, P. R. China |
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| Abstract: | 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.Supported by the National Science Foundation of China Grant No. 10461003. |
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| Keywords: | connecting orbit homoclinic orbit positively bounded system |
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