On the number of isolating integrals in perturbed Hamiltonian systems with \(n\geq 3\) degrees of freedom. (English) Zbl 0842.70008
Summary: We consider a perturbed Hamiltonian system with \(n\geq 3\) degrees of freedom of the form \(H= H_0+ \varepsilon H_1\) and show that the properties of the average value of the perturbing function \(H_1\) along the periodic orbits of the unperturbed integrable part \(H_0\) supply criteria for non-integrability which restrict the allowed total number of independent integrals of motion.
MSC:
| 70H05 | Hamilton’s equations |
| 37J40 | Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion |
