Lower and upper bounds for the splitting of separatrices of the pendulum under a fast quasiperiodic forcing
Visualitza/Obre
Estadístiques de LA Referencia / Recolecta
Inclou dades d'ús des de 2022
Cita com:
hdl:2117/879
Tipus de documentArticle
Data publicació1997
Condicions d'accésAccés obert
Llevat que s'hi indiqui el contrari, els
continguts d'aquesta obra estan subjectes a la llicència de Creative Commons
:
Reconeixement-NoComercial-SenseObraDerivada 2.5 Espanya
Abstract
Quasiperiodic perturbations with two frequencies $(1/\varepsilon ,\gamma /\varepsilon )$ of a pendulum are considered, where $\gamma $ is the golden mean number. We study the splitting of the three-dimensional invariant manifolds associated to a two-dimensional invariant torus in a neighbourhood of the saddle point of the pendulum. Provided that some of the Fourier coefficients of the perturbation (the ones associated to Fibonacci numbers) are separated from zero, it is proved that the invariant manifolds split for $\varepsilon $ small enough. The value of the splitting, that turns out to be ${\rm O} (\exp (-{\rm const} /\sqrt{\varepsilon }) )$, is correctly predicted by the Melnikov function.
Fitxers | Descripció | Mida | Format | Visualitza |
---|---|---|---|---|
9702delsh.pdf | 217,1Kb | Visualitza/Obre |