Stability of equilibrium solutions of Hamiltonian systems under the presence of a single resonance in the non-diagonalizable case |
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Authors: | F. dos Santos C. Vidal |
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Affiliation: | 1. Departamento de Matemática, Universidade Federal de Sergipe, Av. Marechal Rondon, s/n Jardim Rosa Elze, S?o Cristóv?o, SE, Brazil 2. Departmento de Matemática, Facultad de Ciencias, Universidad del Bio Bio, Casilla 5-C, Concepción, VIII-Región, Chile
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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]. |
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Keywords: | Hamiltonian system stability normal form resonances |
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