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A survey on homoclinic and heterocolinic orbits. (English) Zbl 1028.34045
Summary: The study of homoclinic and heteroclinic orbits has a long history. This paper surveys some of the recent advances in this topic. We present some of the main results obtained in recent years, and in addition, we indicate some possible research directions and some problems for further studies.

MSC:
34C37 Homoclinic and heteroclinic solutions to ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
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