Mel’nikov’s Function for Two-Dimensional Mappings
- 1 June 1989
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Applied Mathematics
- Vol. 49 (3) , 692-703
- https://doi.org/10.1137/0149040
Abstract
This paper calculates explicitly the Mel’nikoV function for general perturbations of two-dimensional maps possessing a saddle connection. This result may be considered as the discrete analogue of Ziglin’s calculation of the Mel’nikoV function for time-periodic perturbations of two-dimensional continuous flows.Key words. integrable planar maps, perturbations, homoclinic orbits, Mel'nikoV's function, Poisson summation formulaKeywords
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