Snrvey of the Current Research on HomoclinicOrbits and Heteroclinic Orbits
Received:December 29, 1991  
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Author NameAffiliation
Feng Beiye Inst. of Appl. Math.
Academia Sinica
Beijing 
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Abstract:
      The bifurcation near a homoclinc orbit or a heteroclinic orbit has been interesting thenathematicians in recent years. This paper surveys the recent advance in the research onthis topic from four aspects; I. the existence of the homoclinic orbits and the heteroclinc。rbits; II. the stability of a homoclinc cycle or a heteroclinic cycle; III. the mutual positionbetween the stable manifold and the unstable manifold of a saddle point; IV。 the bifur-cation of a homoclinc orbit or a heteroclinic orbit. We especially survey some important results obtained by Russian and Chinese mathematicians. Some research dircections and problems are suggested for further study.
Citation:
DOI:10.3770/j.issn:1000-341X.1994.02.029
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