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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Moser J. Stable and random motions in dynamical systems [A] In: Annals of Mathematics Studies[C].77 Princeton University Press, Princeton NJ,1973.
Wiggins S. Global Bifurcations and Chaos, Analytic Methods [M]. Springer-Verlag, New York, 1988.
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.
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.
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
Contributed by GUO Bo-ling
Project supported by the National Natural Science Foundation of China (No. 10471046) and the Natural Science Foundation of Guangdong Province of China (No.04300099)
Rights and permissions
About this article
Cite this article
Gao, P., Guo, Bl. Smale horseshoes and chaos in discretized perturbed NLS systems(I)—Poincaré map. Appl. Math. Mech.-Engl. Ed. 26, 1391–1401 (2005). https://doi.org/10.1007/BF03246244
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF03246244