This question is from Elaydi's Discrete Chaos, page 228: Let $f: R^{2} \rightarrow R^{2} $ be given by $f(x,y)= (\frac{x}{2}, 2y- \frac{15}{8} x^{3}) $.
a) Show that the origin is a saddle point of $Df(0)$ (I have done that part).
b) Find the stable and unstable manifold $W^{s}(0)$ and $W^{u}(0)$
c) Find the conjugacy homeomorphism between $f$ and $Df(0)$.
d) Identify the heteroclinic points of $f$.
I haven't found similar examples, so I don't know how to do parts b), c) and d). Can someone do any of these parts and explain how to find stable and unstable manifold in general? Thanks in advance.