 05431 A. GONZALEZENRIQUEZ
 A nonperturbative theorem on conjugation of torus diffeomorphisms to rigid rotations
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Dec 21, 05

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Abstract. The problem of conjugation of torus
diffeomorphisms to rigid rotations is considered here.
Rather than assuming that the diffeomorphisms
are close to rotations,
we assume that the conjugacy equation has an
approximate solution.
First, it is proved that if the rotation vector is Diophantine
and the invariance error function
of the approximate solution has sufficiently small norm,
then there exists a true solution nearby.
The previous result is used to prove that
if an element of a family of diffeomorphisms
$\{\, f_{\mu}\}_{\mu}$ is conjugated to a
rigid rotation with Diophantine rotation vector,
then there exists a Cantor set $\calC$ of parameters such that
for each $\mu\in\calC$ the diffeomorphism $f_{\mu}$ is conjugated
to a Diophantine rigid rotation with rotation vector
that depends on $\mu\in\calC$ in a Whitneysmooth way.
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