We consider the hamiltonian $H=1/2(I_1^2+I_2^2)+\varepsilon(\cos\varphi_1-1)
(1+\mu(\sin\varphi_2+\cos t))$ $I\in\mathbb{R}^2$
("Arnol'd model about diffusion"); by means of
fixed point theorems,
the existence of the stable and unstable manifolds
(whiskers) of invariant, "a priori unstable
tori", for any vector-frequency $(\omega,1)\in\mathbb{R}^2$ is proven.
Our aim is to provide detailed proofs which are missing in Arnol'd's paper,
namely prove
the content of the Assertion B pag.583 of [A]. Our proofs are based on
technical tools suggested by Arnol'd i.e.
the contraction mapping method together
with the "conical metric" (see the footnote
** of pag. 583 of [A]).