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.

Unstable equilibria of Hamiltonian systems / A. Giorgilli. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - 7:4(2001), pp. 855-871.

Unstable equilibria of Hamiltonian systems

A. Giorgilli
Primo
2001

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.
Settore MAT/07 - Fisica Matematica
Article (author)
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/15152
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 21
  • ???jsp.display-item.citation.isi??? 20
social impact