Data di Pubblicazione:
2001
Citazione:
Unstable equilibria of Hamiltonian systems / A. Giorgilli. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - 7:4(2001), pp. 855-871. [10.3934/dcds.2001.7.855]
Abstract:
It is shown that a Hamiltonian system in the neighbourhood of an equilibrium
may be given a special normal form in case four of the eigenvalues of the linearized system
are of the form λ1,−λ1, λ2,−λ2, with λ1 and λ2 independent over the reals, i.e., λ1/λ2 /∈
R. That is, for a real Hamiltonian system and concerning the variables x1, y1, x2, y2 the
equilibrium is of either type center–saddle or complex–saddle. The normal form exhibits the
existence of a four–parameter family of solutions which has been previously investigated by
Moser. This paper completes Moser’s result in that the convergence of the transformation
of the Hamiltonian to a normal form is proven.
Tipologia IRIS:
01 - Articolo su periodico
Elenco autori:
A. Giorgilli
Link alla scheda completa: