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Existence of Diffusion Orbits in a Lattice System

Existence of Diffusion Orbits in a Lattice System
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摘要 We study a model which is a periodic lattice system with nearest neighbors coupling. Using the variational methods, we show the existence of diffusion orbits under a generic perturbation of time periodic. We study a model which is a periodic lattice system with nearest neighbors coupling. Using the variational methods, we show the existence of diffusion orbits under a generic perturbation of time periodic.
作者 Ji LI
机构地区 Department of Mathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2013年第6期1075-1088,共14页 数学学报（英文版）
关键词 Hamiltonian system lattice system Aubry-Mather theory variational methods Hamiltonian system, lattice system, Aubry-Mather theory, variational methods
分类号 O175.2 [理学—基础数学]
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参考文献14

  • 1Arnold, V. I.: Instability of dynamical systems with several degrees of freedom. Soviet Math., 5, 581-585 (1964).
  • 2Delshams, A., de la Llave, R., Seara, T. M.: Geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: heuristic and rigorous verification of a model. Momoirs Amer. Math. Soc., 179(844), 1-141 (2006).
  • 3Cheng, C.-Q., Yan, J.: Existence of diffusion orbits in a priori unstable Hamiltonian systems. J. Differential Geom., 67, 457-517 (2004).
  • 4Cheng, C.-Q., Yan, J.: Arnold diffusion in Hamiltonian Systems: a priori unstable case. J. Differential Geom., 82, 229-277 (2009).
  • 5Colliander, J., Keel, M., Staffilani, G., et al.: Transfer of energy to high frequencies in the cubic defocousing nonlinear SchrSdinger equation. Invent. Math., 181, 39-113 (2010).
  • 6Li, X., Cheng, C.-Q.: Connecting orbits of autonomous Lagrangian systems. Nonlinearity, 23, 119-141 (2010).
  • 7Li, Y. C.: Arnold diffusion of the discrete nonlinear Schrodinger equation. Dynamics PDE, 3, 235-258 (2006).
  • 8Kaloshin, V., Levi, M., Saprykina, M.: Arnold diffusion in a pendulum lattice. Preprint.
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Acta Mathematica Sinica,English Series
2013年 第6期

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