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Exponentially small asymptotic estimates for the splitting of separatrices to whiskered tori with quadratic and cubic frequencies

Autor
Delshams, A.; Gonchenko, M.; Gutiérrez, P.
Tipus d'activitat
Document cientificotècnic
Data
2013
Codi
[prepr201310DelGG]
Repositori
http://hdl.handle.net/2117/20156 Obrir en finestra nova
URL
https://www.ma1.upc.edu/recerca/preprints/preprints-2013/Fitxers/prepr201301gutierrez.pdf Obrir en finestra nova
Resum
We study the splitting of invariant manifolds of whiskered t ori with two or three frequencies in nearly-integrable Hamiltonian systems. We consider 2-dimensional tori with a frequency vector ω = (1 , Ω) where Ω is a quadratic irrational number, or 3-dimensional tori with a frequency v ector ω = (1 , Ω , Ω 2 ) where Ω is a cubic irrational number. Applying the Poincar ́e–Melnikov method, we find exponentia lly small asymptotic estimates for the maximal splitting distance between t...
Citació
Delshams, A.; Gonchenko, M.; Gutiérrez, P. "Exponentially small asymptotic estimates for the splitting of separatrices to whiskered tori with quadratic and cubic frequencies". 2013.
Paraules clau
Melnikov integrals, quadratic and cubic frequencies, splitting of separatrices
Grup de recerca
EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
SD - Sistemes Dinàmics de la UPC

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