Problem 1. Given a 2D system T = 2r 1y, Yy =rz+ 2y, answer the following questions: (a) find the special r such that the 2D system becomes a Hamiltonian dynamics and its corresponding Hamiltonian H(x,y); (b) for the 2D system with the special r, find all the fixed points and their linear stability analysis; (c) determine whether there is a nonlinear center in the Hamiltonian dynamics