Abstract
The aim of this work is to provide asymptotic estimates for the splitting of separatrices in a perturbed 3-degree-of-freedom Hamiltonian system, associated to a two-dimensional whiskered torus (invariant hyperbolic torus) whose frequency ratio is a quadratic irrational number. We show that the dependence of the asymptotic estimates on the perturbation parameter is described by some functions which satisfy a periodicity property, and whose behavior depends strongly on the arithmetic properties of the frequencies.
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Acknowledgements
This work has been partially supported by the Spanish MINECO-FEDER grant number MTM2012-31714 and the Catalan grant 2009SGR859. The author MG has also been supported by the DFG Collaborative Research Center TRR 109 “Discretization in Geometry and Dynamics”.
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Delshams, A., Gonchenko, M., Gutiérrez, P. (2015). A Methodology for Obtaining Asymptotic Estimates for the Exponentially Small Splitting of Separatrices to Whiskered Tori with Quadratic Frequencies. In: Corbera, M., Cors, J., Llibre, J., Korobeinikov, A. (eds) Extended Abstracts Spring 2014. Trends in Mathematics(), vol 4. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-22129-8_6
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DOI: https://doi.org/10.1007/978-3-319-22129-8_6
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-22128-1
Online ISBN: 978-3-319-22129-8
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