Year: 2002
Type: preprint
Abstract: We prove that a Hamiltonian $p\in C^\infty(T^*{\bf R}^n)$ is locally integrable near a non-degenerate critical point $ρ_0$ of the energy, provided that the fundamental matrix at $ρ_0$ 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.
Source: arXiv (Cornell University)
Author: Rouleux, M.
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W26365927