Splitting of separatrices for standard and semistandard mappings

We investigate Chirikov's standard mapping which is a model for the onset of nonintegrability in nonlinear Hamiltonian systems. The asymptotic formula (when the deviation from an integrable system is small) for the angle of intersection of separatrices at a homoclinic point is derived on the ba...

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Bibliographic Details
Published in:Physica. D 1989-12, Vol.40 (2), p.235-248
Main Authors: Lazutkin, V.F., Schachmannski, I.G., Tabanov, M.B.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Physics
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Summary:We investigate Chirikov's standard mapping which is a model for the onset of nonintegrability in nonlinear Hamiltonian systems. The asymptotic formula (when the deviation from an integrable system is small) for the angle of intersection of separatrices at a homoclinic point is derived on the basis of approximation by the Green-Percival semistandard mapping in the complex domain. Computed data on the splitting of separatrices for the semi-standard map are presented from which we derive the pre-exponential coefficient in the formula for splitting of separatrices in the standard mapping.
ISSN:0167-2789
1872-8022
DOI:10.1016/0167-2789(89)90065-1