Unstable equilibria of Hamiltonian systems
by Antonio Giorgilli


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 $\lambda_1,-\lambda_1,\lambda_2,-\lambda_2$, with $\lambda_1$ and $\lambda_2$ independent over the reals, i.e., $\lambda_1/\lambda_2\notin\reali$. That is, for a real Hamiltonian system and concerning the variables $x_1,y_1,x_2,y_2$ the equilibrium is of either type {\it center--saddle} or {\it 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.


DCDS, to appear.


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