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Section: New Results

Orbital stability

In [19], S. De Bièvre and S. Rota Nodari consider the orbital stability of relative equilibria of Hamiltonian dynamical systems on Banach spaces, in the presence of a multi-dimensional invariance group for the dynamics. They prove a persistence result for such relative equilibria, present a generalization of the Vakhitov-Kolokolov slope condition to this higher dimensional setting, and show how it allows to prove the local coercivity of the Lyapunov function, which in turn implies orbital stability. The method is applied to study the orbital stability of relative equilibria of nonlinear Schrödinger and Manakov equations. A comparison of their approach to the one by Grillakis-Shatah-Strauss is provided.