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Transversality of homoclinic orbits to hyperbolic equilibria in a Hamiltonian system, via the Hamilton-Jacobi equation

Autor
Delshams, A.; Gutiérrez, P.; Pacha, Juan R
Tipus d'activitat
Document cientificotècnic
Data
2012-07
Codi
[prepr201202DelGP]
Repositori
http://hdl.handle.net/2117/17084 Obrir en finestra nova
URL
http://www.ma1.upc.edu/recerca/preprints/preprints-2012/Fitxers/prepr201201gutierrez.pdf Obrir en finestra nova
Resum
The key point of our approach is to write the invariant manifolds in terms of generating functions, which are solutions of the Hamilton-Jacobi equation. In some examples, we show that it is enough to analyse the phase portrait of the Riccati equation without solving it explicitly. Finally, we consider an analogous problem in a perturbative situation. If the invariant manifolds of the unperturbed loop coincide, we have a problem of splitting of separatrices. In this case, the Riccati equation is ...
Citació
Delshams, A.; Gutierrez, P.; Pacha, J. "Transversality of homoclinic orbits to hyperbolic equilibria in a Hamiltonian system, via the Hamilton-Jacobi equation". 2012.
Paraules clau
Transverse Homoclinic Orbits, Hyperbolic Equilibria, Hamilton{jacobi Equation, Riccati Equations, Splitting Of Separatrices, Melnikov Integr
Grup de recerca
SD - Sistemes Dinàmics

Arxius