Integrability, hyperbolic flows and the Birkhoff normal form
Rouleux, M.
HAL, hal-00126176 / Harvested from HAL
Text on HAL
We prove that a Hamiltonian $p\in C^\infty(T^*{\bf R}^n)$ is locally integrable near a non-degenerate critical point $\rho_0$ of the energy, provided that the fundamental matrix at $\rho_0$ has no purely imaginary eigenvalues. This is done by using Birkhoff normal forms, which turn out to be convergent in the $C^\infty$ sense. We also give versions of the Lewis-Sternberg normal form near a hyperbolic fixed point of a canonical transformation. Then we investigate the almost holomorphic case.
Publié le : 2004-07-05
Classification:  [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS],  [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] 
@article{hal-00126176,
     author = {Rouleux, M.},
     title = {Integrability, hyperbolic flows and the Birkhoff normal form},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00126176}
}

Rouleux, M. Integrability, hyperbolic flows and the Birkhoff normal form. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00126176/