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Invariant tori for asymptotically linear impact oscillators 被引量：5

Invariant tori for asymptotically linear impact oscillators
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摘要 The existence of invariant tori and quasi-periodic solutions for asymptotically linear impact oscillators is proved by using the successor map and some generalized versions of the Moser's twist theorem. The existence of invariant tori and quasi-periodic solutions for asymptotically linear impact oscillators is proved by using the successor map and some generalized versions of the Moser's twist theorem.
作者 QIAN Dingbian & SUN Xiying School of Mathematical Sciences, Suzhou University, Suzhou 215006, China Laboratory of Mathematics for Nonlinear Sciences, Fudan University, Shanghai 200433, China
出处 《Science China Mathematics》 SCIE 2006年第5期669-687,共19页 中国科学：数学（英文版）
关键词 INVARIANT tori BOUNDEDNESS of solutions QUASI-PERIODIC solution impact oscillator. invariant tori, boundedness of solutions, quasi-periodic solution, impact oscillator.
分类号 TN752 [电子电信—电路与系统]
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参考文献25

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同被引文献15

  • 1LIU Bin Laboratory of Mathematics and its Applications School of Mathematical Sciences Peking University Beijing 100871China.The stability of equilibrium of quasi-periodic planar Hamiltonian and reversible systems[J].Science China Mathematics,2010,53(1):125-136. 被引量：4
  • 2Bonheune D, Fabry C. Periodic motions in impact oscillators with perfectly elastic bouncing [ J ]. Nonlinearity, 2002, 15(4) :1281 - 1298.
  • 3Ortega R. Dynamics of a forced oscillator having an obstacle[ M]//Benci V, Cerami G, Degiovanni M, et al. Variational and Topological Methods in the Study of Nonlinear Phenomina. Boston: Birkhaser, 2002 : 75 - 87.
  • 4Zharnitsky V. Invariant tori in Hamiltonian systems with impacts [ J ]. Communications Mathematical Physics, 2000, 211(2) : 289 -302.
  • 5Qian D B, Tortes P J. Bouncing solutions of an equation with attractive singularity [ C ]//Proceedings of the Royal Society. Edinburgh: [ s. n. ], 2004:201 -213.
  • 6Qian D B ,Torres P J. Periodic motions of linear impact oscillators via the successor map [ J ]. SIAM Journal on Mathematical Analysis, 2005, 36 (6) : 1707 - 1725.
  • 7Chang K C. The obstacle problem and partial differential equations with discontious nonlinerities [ J ]. Communications on Pure and Applied Mathematics, 1980, 33 (2) : 117 - 146.
  • 8Chang K C. Varitional methods for non-differentiable functionals and their applications to partial equations [ J]. Journal of Mathematical Analysis Application, 1981, 80 (1) :102 -129.
  • 9Ding W, Qian D B. Infinitesimal periodic solutions of impact Hamiltonian systems[ J]. Scientia Sinica Mathematica, 2010, 40(6) :563 -574.
  • 10Jiang M Y. Periodic solutions of second order differential equations with an obstacle[ J]. Nonlinearity, 2006, 19 (5) :1165 - 1183.

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Science China Mathematics
2006年 第5期

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