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DEGENERATED HOMOCLINIC BIFURCATIONS WITH HIGHER DIMENSIONS
作者姓名:JIN Yinlai  ZHU Deming
作者单位:JIN YINLAI(Department of Mathematica,East China Normal University,Shanghai 200062,China.)(Department of Mathematics,Linyi Teacher College,Linyi 276005,Shandong,China.) ZHU DEMING(Department of Mathematics,Linyi Teacher College,Linyi 276005,Shan
基金项目:National Natural Science Foundation of China!(No. 19771037)
摘    要:91.IntroductionandHypothesesInrecelltyears)withthedevelopmelltofnonlinearscienceandthedeepstudyof~icphenomena,anincreasinglylargenUInberofpapersared~edtothebifurcationProblemsofhomocliulcandheterocbocorbitsinhighdhansionalspace(see11--14]).Duetothedifficultyencountered,uofortunately,onlyafew(e.g.1,13,14])areconcernedwiththeperiodicorbitsbifulcatedfromsingularloops.Papers1,131discussedtheProblemofthehomoclinicloOPbifurcationinhighdimensionwithcodimension2,thatis,thesystemhasresonanteigenVa…

关 键 词:同宿轨  周期轨道  庞加莱映射  共振
收稿时间:7 June 1999
修稿时间:1999/10/25 0:00:00

DEGENERATED HOMOCLINIC BIFURCATIONS WITH HIGHER DIMENSIONS
JIN Yinlai,ZHU Deming.DEGENERATED HOMOCLINIC BIFURCATIONS WITH HIGHER DIMENSIONS[J].Chinese Annals of Mathematics,Series B,2000,21(2):201-210.
Authors:JIN Yinlai and ZHU Deming
Institution:1. Department of Mathematics, East China Normal University, Shanghai 200062, China;Department of Mathematics, Linyi Teacher College, Linyi 276005, Shandong, China
2. Department of Mathematics, East China Normal University, Shanghai 200062, China
Abstract:The degenerated homoclinic bifurcation for high dimensional system is considered. The existence, uniqueness, and incoexistence of the 1-homclinic orbit and 1-periodic orbit near Γ are studied under the nonresonant condition. Complicated bifurcation pattern is described under the resonant condition. Project supported by the National Natural Science Foundation of China (No. 19771037).
Keywords:Local coordinates  Poincare map  Homoclinic orbit  Periodic orbit  2-fold periodic orbit  Resonant condition
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