Bifurcations of Invariant Tori and Subharmonic Solutions for Periodic Perturbed Systems 被引量：7

Bifurcations of Invariant Tori and Subharmonic Solutions for Periodic Perturbed Systems

导出

摘要 The time-periodic perturbations of planar Hamiltonian systems are investigated.A necessary condition for the existence of an invariant torus,a sufficient condition for the bifurcation of a unique invariant torus and a subharmonic solution are obtained. The time-periodic perturbations of planar Hamiltonian systems are investigated.A necessary condition for the existence of an invariant torus,a sufficient condition for the bifurcation of a unique invariant torus and a subharmonic solution are obtained.

作者韩茂安

机构地区 Department of Mathematics

出处《Science China Mathematics》 SCIE 1994年第11期1325-1336,共12页 中国科学：数学（英文版）

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

关键词 PERIODIC PERTURBED system INVARIANT TORUS SUBHARMONIC solution. periodic perturbed system,invariant torus,subharmonic solution.

分类号 O411.1 [理学—理论物理]

引文网络
相关文献

同被引文献8

1HAN Mao'an CHEN Xianfeng.Existence and bifurcation of integral manifolds with applications[J].Science China Mathematics,2005,48(7):940-957. 被引量：3
2赵育林,张芷芬,李伟固,李承治.Linear estimate of the number of zeros of Abelian integrals for quadratic centers having almost all their orbits formed by cubics[J].Science China Mathematics,2002,45(8):964-974. 被引量：16
3HANMAOAN,BIPING.BIFURCATION OF LIMIT CYCLES FROM A DOUBLE HOMOCLINIC LOOP WITH A ROUGH SADDLE[J].Chinese Annals of Mathematics,Series B,2004,25(2):233-242. 被引量：3
4LIUXUANLIANG HANMAOAN.BIFURCATION OF PERIODIC ORBITS OF A THREE-DIMENSIONAL SYSTEM[J].Chinese Annals of Mathematics,Series B,2005,26(2):253-274. 被引量：5
5韩茂安.LIAPUNOV CONSTANTS AND HOPF CYCLICITYOF LIENARD SYSTEMS[J].Annals of Differential Equations,1999,15(2):113-126. 被引量：8
6HAN Mao’anDepartment of Mathematics, Shanghai Jiaotong University, Shanghai 200030, China.Periodic perturbation of planar systems with a semistable limit cycle[J].Chinese Science Bulletin,1997,42(4):265-270. 被引量：1
7韩茂安,叶彦谦.ON THE COEFFICIENTS APPEARING IN THE EXPANSION OF MELNIKOV FUNCTIONS IN HOMOCLINIC BIFURCATIONS[J].Annals of Differential Equations,1998,14(2):58-64. 被引量：4
8韩茂安.Bifurcation theory of invariant tori of planar periodic perturbed systems[J].Science China Mathematics,1996,39(5):509-519. 被引量：2

引证文献7

1赵育林,张芷芬,李伟固,李承治.Linear estimate of the number of zeros of Abelian integrals for quadratic centers having almost all their orbits formed by cubics[J].Science China Mathematics,2002,45(8):964-974. 被引量：16
2HAN,Mao-an(韩茂安),GU,Sheng-shi(顾圣士).BIFURCATIONS OF SUBHARMONIC SOLUTIONS IN PERIODIC PERTURBATION OF A HYPERBOLIC LIMIT CYCLE[J].Applied Mathematics and Mechanics(English Edition),2002,23(8):981-986.
3叶志勇,韩茂安.一类奇摄动系统奇异极限环的不变环面分支[J].数学年刊（A辑）,2006,27(4):449-458.
4Zhiyong YE,Maoan HAN.Bifurcations of Invariant Tori and Subharmonic Solutions of Singularly Perturbed System[J].Chinese Annals of Mathematics,Series B,2007,28(2):135-148. 被引量：4
5赵丽琴.三次系统中13个极限环的一种新分布[J].北京师范大学学报（自然科学版）,2012,48(3):231-234.
6苗稼乐,杨俊敏.Melnikov函数在含有两个幂零尖点的双异宿环附近的展开式[J].上海师范大学学报（自然科学版）,2020,49(3):295-310.
7ZHANGTong-hua ZANGHong HANMao-an.The Upper Bound of the Number of Limit Cycles of a Classof Non-Hamiltonian Integrable Systems[J].应用数学,2004,17(2):186-191. 被引量：3

二级引证文献22

1李宝毅,谭蕾.一类平面可积系统的Abel积分的化简[J].天津师范大学学报（自然科学版）,2004,24(4):53-55. 被引量：1
2李宝毅,谭蕾.一类平面可积非Hamilton系统的Abel积分[J].天津师范大学学报（自然科学版）,2005,25(2):33-37.
3叶星旸,陈永雪,李学鹏.一类二次系统的Abelian积分的零点数目[J].福建师范大学学报（自然科学版）,2006,22(2):16-20.
4邵仪,赵育林.一类双中心平面二次系统的Abel积分零点个数[J].数学学报（中文版）,2007,50(2):451-460. 被引量：5
5欧阳资考.一类Liénard方程闭轨的不存在性[J].内江师范学院学报,2007,22(4):25-27. 被引量：3
6岳喜顺,孙巍,曾宪武.Bogdanov-Takens系统的一类三次扰动(Ⅰ)[J].数学年刊（A辑）,2008,29(2):261-272. 被引量：4
7黎明.一类二次可逆系统周期函数的单调性[J].数学的实践与认识,2008,38(15):225-230.
8赵育林,陈海波.一类可积非哈密顿系统的极限环数目的上界[J].大学数学,2008,24(5):34-37.
9Feng XIE,Maoan HAN.Existence of Canards under Non-generic Conditions[J].Chinese Annals of Mathematics,Series B,2009,30(3):239-250. 被引量：1
10刘宣亮,孟笑莹.三维系统中一族闭轨在周期扰动下的分支[J].系统科学与数学,2009,29(8):1034-1043. 被引量：2

1HAN,Mao-an(韩茂安),GU,Sheng-shi(顾圣士).BIFURCATIONS OF SUBHARMONIC SOLUTIONS IN PERIODIC PERTURBATION OF A HYPERBOLIC LIMIT CYCLE[J].Applied Mathematics and Mechanics(English Edition),2002,23(8):981-986.
2叶志勇,韩茂安.Periodic Orbits and Invariant Tori from a Semistable Limit Cycle in the Fast Dynamics[J].Journal of Shanghai Jiaotong university(Science),2006,11(1):107-112.
3韩茂安.Bifurcation theory of invariant tori of planar periodic perturbed systems[J].Science China Mathematics,1996,39(5):509-519. 被引量：2
4吴然超,孙建华.HOPF-BIFURCATIONS FOR NONHYPERBOLIC INVARIANT TORI[J].Annals of Differential Equations,2003,19(2):220-228.
5Hui LU,Jian Gong YOU.Two-Dimensional Invariant Tori in the Neighborhood of an Elliptic Equilibrium of Hamiltonian Systems[J].Acta Mathematica Sinica,English Series,2009,25(8):1363-1378.
6Zhiyong YE,Maoan HAN.Bifurcations of Invariant Tori and Subharmonic Solutions of Singularly Perturbed System[J].Chinese Annals of Mathematics,Series B,2007,28(2):135-148. 被引量：4
7LI XIONG.BOUNDEDNESS OF SOLUTIONS FOR SUPERLINEAR REVERSIBLE SYSTEMS[J].Chinese Annals of Mathematics,Series B,2001,22(1):31-46.
8柳彬,王奕倩.Invariant tori in nonlinear oscillations[J].Science China Mathematics,1999,42(10):1047-1058. 被引量：2
9Hai-ping Shi Xue-jun Zhong.Existence of Periodic and Subharmonic Solutions for Second Order Functional Difference Equations[J].Acta Mathematicae Applicatae Sinica,2010,26(2):229-240.
10Bao She WEI Department of Mathematics, Nanjing University. Nanjing 210093. P. R. China.Existence of Invariant Tori for Certain Weakly Reversible Mappings[J].Acta Mathematica Sinica,English Series,2002,18(4):701-718.

Science China Mathematics

1994年第11期

浏览历史

内容加载中请稍等...

Bifurcations of Invariant Tori and Subharmonic Solutions for Periodic Perturbed Systems 被引量：7

同被引文献8

引证文献7

二级引证文献22

相关作者

相关机构

相关主题

浏览历史