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

Autor
Delshams, A.; Gonchenko, M.; Gutiérrez, P.
Tipus d'activitat
Article en revista
Revista
Electronic research announcements in mathematical sciences
Data de publicació
2014-01-01
Volum
21
Pàgina inicial
41
Pàgina final
61
DOI
https://doi.org/10.3934/era.2014.21.41 Obrir en finestra nova
Projecte finançador
DINAMICA ASOCIADA A CONEXIONES ENTRE OBJETOS INVARIANTES, ASTRODINÁMICA, NEUROCIENCIA Y OTRAS APLICACIONES
DINAMICA ASOCIADA A CONEXIONES ENTRE OBJETOS INVARIANTES. APLICACIONES A
Repositori
http://hdl.handle.net/2117/23508 Obrir en finestra nova
URL
http://www.aimsciences.org/journals/pdfs.jsp?paperID=9884&mode=full Obrir en finestra nova
Resum
We study the splitting of invariant manifolds of whiskered tori with two or three frequencies in nearly-integrable Hamiltonian systems, such that the hyperbolic part is given by a pendulum. We consider a 2-dimensional torus with a frequency vector omega = (1, Omega), where Omega is a quadratic irrational number, or a 3-dimensional torus with a frequency vector w = (1, Omega, Omega(2)), where Omega is a cubic irrational number. Applying the Poincare-Melnikov method, we find exponentially small as...
Citació
Delshams, A.; Gonchenko, M.; Gutiérrez, P. Exponentially small asymptotic estimates for the splitting of separatrices to whiskered tort with quadratic and cubic frequencies. "Electronic research announcements in mathematical sciences", 01 Gener 2014, vol. 21, p. 41-61.
Paraules clau
ADIABATIC INVARIANTS, APPROXIMATION, CONTINUED FRACTIONS, INTEGRABLE HAMILTONIAN-SYSTEMS, MCMILLAN MAP, MELNIKOV METHOD, Melnikov integrals, PENDULUM, PERTURBATION, RENORMALIZATION, UPPER-BOUNDS, 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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