Snrvey of the Current Research on HomoclinicOrbits and Heteroclinic Orbits |
Received:December 29, 1991 |
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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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