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Splitting of separatrices in the resonances of nearly integrable Hamiltonian Systems of one and a half degrees of freedom

Autor
Guardia, M.
Tipus d'activitat
Article en revista
Revista
Discrete and continuous dynamical systems. Series A
Data de publicació
2013
Volum
33
Número
7
Pàgina inicial
2829
Pàgina final
2859
DOI
https://doi.org/10.3934/dcds.2013.33.2829 Obrir en finestra nova
Repositori
http://hdl.handle.net/2117/113880 Obrir en finestra nova
Resum
In this paper we consider general nearly integrable analytic Hamiltonian systems of one and a half degrees of freedom which are a trigonometric polynomial in the angular state variable. In the resonances of these systems generically appear hyperbolic periodic orbits. We study the possible transversal intersections of their invariant manifolds, which is exponentially small, and we give an asymptotic formula for the measure of the splitting. We see that its asymptotic first order is of the form Ke...
Citació
Guardia, M. Splitting of separatrices in the resonances of nearly integrable Hamiltonian Systems of one and a half degrees of freedom. "Discrete and continuous dynamical systems. Series A", 2013, vol. 33, núm. 7, p. 2829-2859.
Paraules clau
Complex Matching., Nearly Integrable Hamiltonian Systems, Exponentially Small Splitting Of Separatrices, Melnikov Method.
Grup de recerca
SD - Sistemes Dinàmics de la UPC

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