Consider a system u=g(u,v),v=Cv+h(u,v), with uR,vRc. We assume that g(u,v)=O(u2+v2) and h(u,v)=O(u2+v2), and that the matrix C is hyperbolic. As discussed in class, there exists a center manifold v=(u) for u near zero, with (0)=0 and (0)=0, and which therefore has a Taylor series (u)=2u2+3u3+O(u4). We may write g(u,0)=u2+O(u3)h(u,v)=2u2+uLv+3u3+O(v2)+O(u2v+uv2+v3)+O(u4+v4), where R,2,3Rc,L:RcRcislinear. 2=C12. (You may use this fact.) (a) Justify the above formula for h(u,v), that is, verify that the various order relations O() are correct. (b) Calculate the value of 3