Let M be a smooth manifold, $f$ a diffeomorphism on M and for $p, q \in M$ consider $W^s_p$ the stable manifold in $p$ (i.e. the set of points whose forward orbit tend to the forward orbit of $p$) and $W^u_q$ the unstable manifold in $q$ (i.e. the set of points whose backward orbit tends to backward orbit of $q$).
I don't understand why $W^s_p$ intersects $ W^u_q$. Can someone explain me, please?
P.S. In my case, p is a fixed point and q a periodic point.