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Continuation of the exponentially small lower bounds for the splitting of separatrices to a whiskered torus with silver ratio

Autor
Delshams, A.; Gonchenko, M.; Gutiérrez, P.
Tipus d'activitat
Document cientificotècnic
Data
2014-09
Codi
[prepr201404DelGG]
Projecte finançador
DINAMICA ASOCIADA A CONEXIONES ENTRE OBJETOS INVARIANTES. APLICACIONES A
Repositori
http://hdl.handle.net/2117/24138 Obrir en finestra nova
URL
http://www.ma1.upc.edu/recerca/preprints/preprints-2014/preprint-2014 Obrir en finestra nova
Resum
We study the exponentially small splitting of invariant manifolds of whiskered (hyperbolic) tori with two fast frequencies in nearly-integrable Hamiltonian systems whose hyperbolic part is given by a pendulum. We consider a torus whose frequency ratio is the silver number $\Omega=\sqrt2-1$. We show that the oincare-Melnikov method can be applied to establish the existence of 4 transverse homoclinic orbits to the whiskered torus, and provide asymptotic estimates for the tranversality of the split...
Citació
Delshams, A.; Gonchenko, M.; Gutiérrez, P. "Continuation of the exponentially small lower bounds for the splitting of separatrices to a whiskered torus with silver ratio". 2014.
Paraules clau
Melnikov integrals, silver ratio, splitting of separatrices, transverse homoclinic orbits
Grup de recerca
EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
SD - Sistemes Dinàmics de la UPC

Participants

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