Smale Horseshoes and Chaos in Discretized Perturbed NLS Systems(Ⅱ)——Smale Horseshoes

GAO Ping; GUO Bo-ling

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GAO Ping, GUO Bo-ling. Smale Horseshoes and Chaos in Discretized Perturbed NLS Systems(Ⅱ)——Smale Horseshoes[J]. Applied Mathematics and Mechanics, 2005, 26(11): 1271-1277.

Citation:

GAO Ping, GUO Bo-ling. Smale Horseshoes and Chaos in Discretized Perturbed NLS Systems(Ⅱ)——Smale Horseshoes[J]. Applied Mathematics and Mechanics, 2005, 26(11): 1271-1277.

Citation:

GAO Ping, GUO Bo-ling. Smale Horseshoes and Chaos in Discretized Perturbed NLS Systems(Ⅱ)——Smale Horseshoes[J]. Applied Mathematics and Mechanics, 2005, 26(11): 1271-1277.

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Smale Horseshoes and Chaos in Discretized Perturbed NLS Systems(Ⅱ)——Smale Horseshoes

GAO Ping¹,
GUO Bo-ling²

1.
Department of Applied Mathematics, Guangzhou University, Guangzhou 510405, P. R. China;

Received Date: 2004-08-08
Rev Recd Date: 2005-08-23
Publish Date: 2005-11-15

Abstract

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 Lambda on which the dynamics is topologically conjugate to a shift on four symbols.
- homoclinic orbit,
- Poincaré map,
- Smale horseshoes,
- Conley-Moser condition

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References(3)

References

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[2]	Wiggins S.Global Bifurcations and Chaos, Analytic Methods[M].New York:Springer-Verlag,1988.
[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. doi: 10.1007/BF02678141