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2013
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# Fabio Dos Santos

Av. prof. Luiz Freire, s/n, CEP 50740-540, Pernambuco, Brazil
Departamento de Matematica, Universidade Federal de Pernambuco

## Publications:

 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 Abstract 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 [1]. Keywords: Hamiltonian system, stability, normal form, resonances Citation: Dos Santos F., Vidal C.,  Stability of Equilibrium Solutions of Hamiltonian Systems Under the Presence of a Single Resonance in the Non-Diagonalizable Case, Regular and Chaotic Dynamics, 2008, vol. 13, no. 3, pp. 166-177 DOI:10.1134/S1560354708030039
 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 Abstract 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. Keywords: periodic Hamiltonian system, Lyapunov stability, formal stability, resonance, normal form Citation: Vidal C., Dos Santos F.,  Stability of equilibrium positions of periodic Hamiltonian systems under third and fourth order resonances , Regular and Chaotic Dynamics, 2005, vol. 10, no. 1, pp. 95-111 DOI: 10.1070/RD2005v010n01ABEH000303