 97478 Paolo Perfetti
 Fixed point theorems in the Arnol'd model about instability of the
actionvariables in phasespace
(55K, amstex)
Sep 8, 97

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Abstract. We consider the hamiltonian $H={1\over2}(I_1^2+I_2^2)+\varepsilon(\cos\varphi_11)
(1+\mu(\sin\varphi_2+\cos t))$ $I\in{\Bbb R}^2$
(\lq\lq Arnol'd model about diffusion"); by means of
fixed point theorems,
the existence of the stable and unstable manifolds
{\it (whiskers)} of invariant, \lq\lq a priori unstable
tori", for any vectorfrequency $(\omega,1)\in{\Bbb R}^2$ is proven.
Our aim is to provide detailed proofs which are missing in Arnol'd's paper,
namely prove
the content of the {\tt Assertion B} pag.583 of [A]. Our proofs are based on
technical tools suggested by Arnol'd i.e.
the contraction mapping method togheter
with the \lq\lq conical metric" ( see the footnote
** of pag. 583 of [A]). }
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