Berwald-moor metrics and structural stability of conformally-deformed geodesic SODE.
Let be a real algebraic number of degree over whose conjugates are not real. There exists an unit of the ring of integer of for which it is possible to describe the set of all best approximation vectors of .’
We prove existence of small amplitude, 2p/v-periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions for any frequency belonging to a Cantor-like set of positive measure and for a generic set of nonlinearities. The proof relies on a suitable Lyapunov-Schmidt decomposition and a variant of the Nash-Moser Implicit Function Theorem.