Equivariant Lyapunof Center Theorem

We prove the existence of small amplitude quasi- periodic solutions of some nonlinear Hamiltonian partial differential equations, exploiting the symmetries of the systems. Our theorem is obtained requiring a Dyophantine type nonresonance condition, a standard nondegeneracy condition and assuming a regularizing property of the nonlinearity. The proof is based on the Lyapunov-Schmidt reduction method, a suitable analysis of small denominators and on the standard implicit function theorem. We apply our result to the nonlinear beam equation with spatial periodic boundary conditions, to a beam vibrating in a two dimensional space with Dirichlet boundary conditions and to the nonlinear wave equation with spatial periodic boundary conditions.

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Cristina Bardelle completed her Ph.D. in Mathematics in 2007 at the Università degli Studi in Milano, under the supervision of Prof. Dario Bambusi. Her present research interests involve mathematics education, focusing on the role of language and visual reasoning in the teaching and learning of mathematics.