Exponential dichotomies and heteroclinic bifurcations in degenerate cases

Exponential dichotomies and heteroclinic bifurcations in degenerate cases

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摘要 By making use of theory of exponential dichotomies, the theory of heteroclinic bifurcations in higher degenerate cases is investigated. A Melnikov-type vector is given by which the existence of transversal heteroclinic orbits in degenerate cases can be detected. A functional analytical method of proving the transver-sality of heteroclinic orbits in degenerate cases is also provided. By making use of theory of exponential dichotomies, the theory of heteroclinic bifurcations in higher degenerate cases is investigated. A Melnikov-type vector is given by which the existence of transversal heteroclinic orbits in degenerate cases can be detected. A functional analytical method of proving the transver-sality of heteroclinic orbits in degenerate cases is also provided.

作者曾唯尧井竹君

机构地区 Hunan Light Industrial College Institute of Mathematics

出处《Science China Mathematics》 SCIE 1995年第6期653-661,共9页 中国科学：数学（英文版）

基金 Project supported by the National Natural Science Foundation of China.

关键词 EXPONENTIAL dichotomies HETEROCLINIC ORBITS DEGENERATE case MELNIKOV vector. exponential dichotomies, heteroclinic orbits, degenerate case, Melnikov vector.

分类号 O177.3 [理学—基础数学]

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1杨文熊.POWER VECTORS,COMBINATORIAL VECTOR NUMBERS AND ITS THEORY OF FUNCTIONS[J].Applied Mathematics and Mechanics(English Edition),1996,17(2):139-144.
2曾唯尧,钱祥征,王志成.EXPONENTIAL DICHOTOMIES,HOMOCLINIC ORBITS AND METHODS OF MELNIKOV[J].Acta Mathematica Scientia,1996,16(1):113-120.
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5张伟年.NOTES ON GENERALIZED EXPONENTIAL DICHOTOMIES[J].Acta Mathematicae Applicatae Sinica,1996,12(4):384-392.
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9孙建华.Equivalence of two Melnikov functions[J].Chinese Science Bulletin,1996,41(8):626-630.
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Science China Mathematics

1995年第6期

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Exponential dichotomies and heteroclinic bifurcations in degenerate cases

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