#### Abstract

1. Compute the center manifold (to second order), and the reduced system on it (to third order), and conclude regarding the behavior of the systems near the origin (draw phase portrait) for F(x, y) = (x + xy − y 2 , 1 2 y + x 2). Solution. Let us write the map in the form: x n+1 = x n + x n y n − y 2 n y n+1 = 1 2 y n + x 2 n (1) Note that the origin (0, 0… (More)