Singular separatrix splitting and the Poincare-Melnikov method for area preserving maps
Visualitza/Obre
Estadístiques de LA Referencia / Recolecta
Inclou dades d'ús des de 2022
Cita com:
hdl:2117/771
Tipus de documentArticle
Data publicació1999
Condicions d'accésAccés obert
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Reconeixement-NoComercial-SenseObraDerivada 2.5 Espanya
Abstract
The splitting of separatrices of area preserving maps close to the identity is one of the most paradigmatic examples of an exponentially small or singular phenomenon. The intrinsic small parameter is the characteristic exponent h > 0 of the saddle fixed point. A standard technique to measure the splitting of separatrices is the so-called Poincaré-Melnikov method, which has several specic features in the case of analytic planar maps. The aim of this talk is to compare the predictions for the splitting of separatrices provided by the Poincaré-Melnikov method, with the analytic and numerical results in a simple example where computations in multiple-precision arithmetic are performed.
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9906delsh.pdf | 159,8Kb | Visualitza/Obre |