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Applied Mathematics and Mechanics

, Volume 26, Issue 11, pp 1391–1401 | Cite as

Smale horseshoes and chaos in discretized perturbed NLS systems(I)—Poincaré map

  • Ping Gao
  • Bo-ling Guo
Article

Abstract

The existence of Smale horseshoes for a certain discretized perturbed nonlinear Schroedinger (NLS) equations was established by using n-dimensional versions of the Conley-Moser conditions. As a result, the discretized perturbed NLS system is shown to possess an invariant set ∧ on which the dynamics is topologically conjugate to a shift on four symbols.

Key words

homoclinic orbit Poincaré map Smale horseshoes Conley-Moser condition 

Chinese Library Classification

O175 

Document code

2000 Mathematics Subject Classification

35Q 

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References

  1. [1]
    Moser J. Stable and random motions in dynamical systems [A] In: Annals of Mathematics Studies[C].77 Princeton University Press, Princeton NJ,1973.Google Scholar
  2. [2]
    Wiggins S. Global Bifurcations and Chaos, Analytic Methods [M]. Springer-Verlag, New York, 1988.CrossRefGoogle Scholar
  3. [3]
    Li Y, Wiggins S. Homoclinic orbits and chaos in discretized perturbed NLS systems: Part II, Symbolic dynamics[J]. J Nonlinear Sci, 1997,7(4):315–370.MathSciNetMATHGoogle Scholar
  4. [4]
    Guo Bo-ling, Chen Han-lin. Persistent homodinic orbits for a perturbed cubic-quintic nonlinear Schrodinger equation[J]. J Partial Diff Eqs, 2002,15 (2): 6–36.Google Scholar
  5. [5]
    Li Y, Wiggins S. Homoclinic orbits and chaos in discretized perturbed NLS systems: Part I, Homoclinic orbits[J]. J Nonlinear Sci, 1997,7(3):211–269.MathSciNetMATHGoogle Scholar

Copyright information

© Editorial Committee of Appl. Math. Mech. 2005

Authors and Affiliations

  1. 1.Department of Applied MathematicsGuangzhou UniversityGuangzhouP. R. China
  2. 2.Institute of Applied Physics and Computational MathematicsBeijingP. R. China

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