Fabio Dos Santos
Av. prof. Luiz Freire, s/n, CEP 50740-540, Pernambuco, Brazil
Departamento de Matematica, Universidade Federal de Pernambuco
Dos Santos F., Vidal C.
Stability of Equilibrium Solutions of Hamiltonian Systems Under the Presence of a Single Resonance in the Non-Diagonalizable Case
2008, vol. 13, no. 3, pp. 166-177
The problem of knowing the stability of one equilibrium solution of an analytic autonomous Hamiltonian system in a neighborhood of the equilibrium point in the case where all eigenvalues are pure imaginary and the matrix of the linearized system is non-diagonalizable is considered.We give information about the stability of the equilibrium solution of Hamiltonian systems with two degrees of freedom in the critical case. We make a partial generalization of the results to Hamiltonian systems with $n$ degrees of freedom, in particular, this generalization includes those in .
Vidal C., Dos Santos F.
Stability of equilibrium positions of periodic Hamiltonian systems under third and fourth order resonances
2005, vol. 10, no. 1, pp. 95-111
The problem of the stability of an equilibrium position of a nonautonomous 2$\pi$-periodic Hamiltonian system with $n$ degrees of freedom ($n \geqslant 2$), in a nonlinear setting, is studied in the presence of a single third and fourth order resonance. We give conditions of instability in the sense of Lyapunov and formal stability of the equilibrium position, depending on the coefficients of the Hamiltonian function.