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Abstract and Applied Analysis
Volume 2011 (2011), Article ID 354063, 17 pages
http://dx.doi.org/10.1155/2011/354063
Research Article

On the Reducibility for a Class of Quasi-Periodic Hamiltonian Systems with Small Perturbation Parameter

Department of Mathematics, Southeast University, Nanjing 210096, China

Received 1 December 2010; Revised 18 April 2011; Accepted 25 May 2011

Academic Editor: Yuri V. Rogovchenko

Copyright © 2011 Jia Li and Junxiang Xu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. N. N. Bogoljubov, J. A. Mitropoliski, and A. M. Samoilenko, Methods of Accelerated Convergence in Nonlinear Mechanics, Springer, New York, NY, USA, 1976.
  2. R. A. Johnson and G. R. Sell, “Smoothness of spectral subbundles and reducibility of quasiperiodic linear differential systems,” Journal of Differential Equations, vol. 41, no. 2, pp. 262–288, 1981. View at Publisher · View at Google Scholar
  3. A. Jorba and C. Simó, “On the reducibility of linear differential equations with quasiperiodic coefficients,” Journal of Differential Equations, vol. 98, no. 1, pp. 111–124, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. L. H. Eliasson, “Floquet solutions for the one-dimensional quasi-periodic Schrödinger equation,” Communications in Mathematical Physics, vol. 146, no. 3, pp. 447–482, 1992. View at Publisher · View at Google Scholar
  5. L. H. Eliasson, “Almost reducibility of linear quasi-periodic systems,” in Smooth Ergodic Theory and Its Applications (Seattle, WA, 1999), vol. 69 of Proceedings of Symposia in Pure Mathematics, pp. 679–705, American Mathematical Society, Providence, RI, USA, 2001. View at Zentralblatt MATH
  6. H.-L. Her and J. You, “Full measure reducibility for generic one-parameter family of quasi-periodic linear systems,” Journal of Dynamics and Differential Equations, vol. 20, no. 4, pp. 831–866, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. A. Jorba and C. Simó, “On quasi-periodic perturbations of elliptic equilibrium points,” SIAM Journal on Mathematical Analysis, vol. 27, no. 6, pp. 1704–1737, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. X. Wang and J. Xu, “On the reducibility of a class of nonlinear quasi-periodic system with small perturbation parameter near zero equilibrium point,” Nonlinear Analysis, vol. 69, no. 7, pp. 2318–2329, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. H. Whitney, “Analytic extensions of differentiable functions defined in closed sets,” Transactions of the American Mathematical Society, vol. 36, no. 1, pp. 63–89, 1934. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. L. Zhang and J. Xu, “Persistence of invariant torus in Hamiltonian systems with two-degree of freedom,” Journal of Mathematical Analysis and Applications, vol. 338, no. 2, pp. 793–802, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. J. Moser, “Convergent series expansions for quasi-periodic motions,” Mathematische Annalen, vol. 169, pp. 136–176, 1967. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. M. B. Sevryuk, “KAM-stable Hamiltonians,” Journal of Dynamical and Control Systems, vol. 1, no. 3, pp. 351–366, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. K. Soga, “A point-wise criterion for quasi-periodic motions in the KAM theory,” Nonlinear Analysis, vol. 73, no. 10, pp. 3151–3161, 2010. View at Publisher · View at Google Scholar