On the discretization of a partial differential equation in the neighborhood of a periodic orbit.
We study the existence of global canard surfaces for a wide class of real singular perturbation problems. These surfaces define families of solutions which remain near the slow curve as the singular parameter goes to zero.
For several specific mappings we show their chaotic behaviour by detecting the existence of their transversal homoclinic points. Our approach has an analytical feature based on the method of Lyapunov-Schmidt.
We study the vector -Laplacian We prove that there exists a sequence of solutions of () such that is a critical point of and another sequence of solutions of such that is a local minimum point of , where is a functional defined below.