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In this paper we study resonances in two degrees of freedom, autonomous, hamil-tonian systems. Due to the presence of a symmetry condition on one of the degrees of freedom, we show that some of the resonances vanish as lower order resonances. After determining the size of the resonance domain, we investigate this order change of resonance in a rather… (More)

- J M Tuwankotta, F Verhulst
- 2001

In this paper we study two degree of freedom Hamiltonian systems and applications to nonlinear wave equations. Near the origin, we assume that near the linearized system has purely imaginary eigenvalues: i! 1 and i! 2 , with 0 < ! 2 =! 1 1 or ! 2 =! 1 1, which is interpreted as a perturbation of a problem with double zero eigenvalues. Using the averaging… (More)

In this paper we study the performance of a symplectic numerical integrator based on the splitting method. This method is applied to a subtle problem i.e. higher order resonance of the elastic pendulum. In order to numerically study the phase space of the elastic pendulum at higher order resonance, a numerical integrator which preserves qualitative features… (More)

- J M Tuwankotta
- 2007

In this paper we present an analysis of a system of coupled oscillators suggested by atmospheric dynamics. We make two assumptions for our system. The first assumption is that the frequencies of the characteristic oscillations are widely separated and the second is that the nonlinear part of the vector field preserves the distance to the origin. Using the… (More)

This paper reviews higher order resonance in two degrees of freedom Hamilto-nian systems. We consider a positive semi-deenite Hamiltonian around the origin. Using normal form theory, we give an estimate of the size of the domain where interesting dynamics takes place, which is an improvement of the one previously known. Using a geometric numerical… (More)

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