Normalization of a Hamiltonian system near an invariant cycle or torus

Semi-classical quantization rules for a periodic orbit of hyperbolic type

“…), (??) BNF holds in the classical sense [5] as well as in the semi-classical sense [15] and takes, modulo a small remainder term, operator H w (y, hD y ; h) to a polynomial in hD t and Q w j (x, hD x ), Q j (x, ξ) as above. In particular, the principal part of H w (y, hD y ; h) is in BNF is given by (??)…”

Periodic rotations of a rigid body located at the libration point

“…We will investigate its orbital stability. The method employed (Brjuno, 1970;Brjuno, 1988;Brjuno, 1989;Markeev, 1975) is based upon normalization procedure of the Hamiltonian in a neighborhood of the periodic solution. It will be performed up to the second order of parameter e, because some effects do not appear if the first order terms are considered only.…”

“…Thus, if parameters ft, e lie on curve (22) then the periodic solution is orbitally unstable (Brjuno, 1989;Markeev, 1975). In nonresonant case all third order terms are removed fl'om Hamiltonian function and stability is determined by fourth order terms.…”

“…where d and cij do not depend on W1 and W2, and : Now, we make use of Arnold-Moser theorem and its modification to the resonance case (Brjuno, 1989;Markeev, 1975 …”

System for normalization of a hamiltonian function based on lie series

“…• finding of periodic and quasi-periodic solutions (Bruno, 1988;Bruno 1989), We have set up a claim that, from technical point of view, the system should have clear 'didactical' form and it should easily allow for its fast modifications.…”