Nekhoroshev-stability of elliptic equilibria of Hamiltonian systems
The paper is devoted to prove the Nekhoroshev conjecture [see \textit{N. N. Nekhoroshev}, Usp. Mat. Nauk 32, No. 6, 5-66 (1977; Zbl 0389.70028) (Sect.2.2)] about the exponential long time stability of elliptic equilibria of Hamiltonian systems without Diophantine assumptions on frequencies. These frequencies are assumed to be nonresonant up to the order 4 and some conditions on the higher order terms of the Hamiltonian which provide the convexity are also required. The singularity of the action-angle coordinates at the origin is overcome by working in Cartesian coordinates.
scientific article; zbMATH DE number 1294585