Abstract
The standard mapping arises in many physical applications, including the analysis of nonlinear resonant acoustic oscillations in a closed tube. A perturbation expansion, in powers of the amplitude parameter, is given for the calculation of the fixed points of various orders and the associated separatrices. It is shown how exact homoclinic orbits can be calculated numerically. Explicit analytic expressions are given for the separatrices associated with the first four resonances when the perturbation parameter is small.
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Mortell, M.P., Seymour, B.R. The calculation of resonance separatrices for the near-integrable case of the standard mapping. Z. angew. Math. Phys. 39, 861–873 (1988). https://doi.org/10.1007/BF00945123
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DOI: https://doi.org/10.1007/BF00945123