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碰撞Hamiltonian系统的无穷小周期解 被引量：3

Infinitesimal periodic solutions of impact Hamiltonian systems
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摘要 本文通过适当的坐标变换将碰撞振子的相平面转变为全平面,应用Poincaré-Birkhoff扭转定理,证明了在原点附近超线性碰撞振子的无穷多弹性周期解的存在性,从而推广了已有的结果. Using a new coordinate transformation for impact oscillators with suplinearity around the orign, we obtain the existence of infinite bouncing periodic solutions by applying the Poincare-Birkhoff twist theorem which improves the previous results.
作者 丁卫 钱定边
机构地区 南通大学理学院 苏州大学数学科学学院
出处 《中国科学：数学》 CSCD 北大核心 2010年第6期563-574,共12页 Scientia Sinica：Mathematica
基金 国家自然科学基金(批准号:10971228 10871142) 南通大学自然科学基金(编号:09Z004)资助项目
关键词 碰撞振子 弹性周期解 POINCARE映射 Poincare-Birkhoff扭转定理 impact oscillators, bouncing periodic solutions, Poincare map, Poincare-Birkhofftwist theorem
分类号 O175 [理学—基础数学]
  • 相关文献

参考文献18

  • 1Lamba H. Chaotic, regular and unbounded behaviour in the elastic impact oscillator. Phys D, 1995, 82:117- 135.
  • 2Boyland P. Dual billards, twist maps and impact oscillators. Nonlinearity, 1996, 9:1411 -1438.
  • 3Corbera M, Llibre J. Periodic orbits of a collinear restricted three body problem. Celestial Mech Dynam Astronom 2003, 86:163-183.
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  • 6Ortega R. Dynamics of a forced oscillator with obstacle. In: Benci Vet al. eds. Variational and Topological methods in the study of nonlinear phenomina. Boston: Birkhaser, 2002, 77 89.
  • 7Bonheune D, Fabry C. Periodic motions in impact oscillators with perfectly elastic bouncing. Nonlinearity, 2002, 15: 1281-1298.
  • 8Qian D, Torres P J. Periodic motions of linear impact oscillators via successor map. SIAM J Math Anal, 2005, 36: 1707-1725.
  • 9Qian D, Torres P J. Bouncing solutions of an equantion with attractive singularity. Proc Roy Soc Edinburgh Sect A, 2004, 134:210-213.
  • 10钱定边,孙西瀅.渐近线性碰撞振子的不变环面[J].中国科学（A辑）,2006,36(4):418-437. 被引量：2

二级参考文献25

  • 1Lamba H.Chaotic,regular and unbounded behaviour in the elastic impact oscillator.Physica D,1995,82:117～135
  • 2Zharnitsky V.Invariant tori in Hamiltonian systems with impacts.Comm Math Phys,2000,211:289～302
  • 3Boyland P.Dual billiards,twist maps and impact oscillators.Nonlinearity,1996,9:1411～1438
  • 4Corbera M,Llibre J.Periodic orbits of a collinear restricted three body problem.Celestial Mech Dynam Astronom,2003,86:163～183
  • 5Kunze M.Non-Smooth Dynamical Systems.Lecture Notes in Math,Vol 1744.New York:SpringerVerlag,2000
  • 6Qian D,Torres P J.Bouncing solutions of an equation with attractive singularity.Proc Roy Soc Edinburgh,2004,134A:210～213
  • 7Bonheure D,Fabry C.Periodic motions in impact oscillators with perfectly elastic bouncing.Nonlinearity,2002,15:1281～1298
  • 8Ortega R.Dynamics of a forced oscillator having an obstacle.In:Benci V,Cerami G,Degiovanni M,et al,eds.Variational and Topological methods in the Sstudy of Nonlinear Phenomena.Progress in Nonlinear Differential Equations,49.Boston:Birkhaser,2001.75～87
  • 9Qian D.Large amplitude periodic bouncing in impact oscillators with damping.Proc Amer Math Soc,2005,133:1797～1804
  • 10Qian D,Torres P J.Periodic motions of linear impact oscillators via the successor map.SIAM J Math Anal,2005,36:1707～1725

共引文献1

同被引文献38

  • 1钱定边,孙西瀅.渐近线性碰撞振子的不变环面[J].中国科学（A辑）,2006,36(4):418-437. 被引量：2
  • 2侯国林,阿拉坦仓,黄俊杰.Hilbert空间线性二次最优控制问题中的一个算子的可逆性[J].数学学报（中文版）,2007,50(2):473-480. 被引量：6
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  • 5Magri F. A simple model of the integrable Hamiltonian equation. J Math Phys, 1978, 19:1156-1162.
  • 6Olver P J. Applications of Lie Groups to Differential Equations. New York: Springer-Verlag, 1998.
  • 7Tretter C. Spectral Theory of Block Operator Matrices and Applications. London: Imperial College Press, 2008.
  • 8Langer H, Ran A C M, van de Rotten B A. Invariant subspaces of infinite dimensional Hamiltonians and Solutions of the corresponding Riccati equations. Oper Theory Adv Appl, 2001, 130:235-254.
  • 9Kurina G A. Invertibility of nonnegatively Hamiltonian operators in a Hilbert space. Differential Equations, 2001, 37: 880-882.
  • 10Langer H, Langer M, Tretter C. Variational principles for eigenvalues of block operator matrices. Indiana Univ Math J, 2002, 51:1427-1458.

引证文献3

二级引证文献9

中国科学：数学
2010年 第6期

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