 06110 Guido Gentile, Michele V. Bartuccelli, Jonathan H.B. Deane
 Quasiperiodic attractors, Borel summability and
the Bryuno condition for strongly dissipative systems
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Apr 7, 06

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Abstract. We consider a class of ordinary differential equations describing
onedimensional analytic systems with a quasiperiodic forcing term
and in the presence of damping. In the limit of large damping,
under some generic nondegeneracy condition on the force, there are
quasiperiodic solutions which have the same frequency vector as the
forcing term. We prove that such solutions are Borel summable at the
origin when the frequency vector is either any onedimensional
number or a twodimensional vector such that the ratio of its
components is an irrational number of constant type.
In the first case the proof given simplifies that provided
in a previous work of ours. We also show that in any dimension $d$,
for the existence of a quasiperiodic solution with the same
frequency vector as the forcing term, the standard Diophantine
condition can be weakened into the Bryuno condition.
In all cases, under a suitable positivity condition, the
quasiperiodic solution is proved to describe a local attractor.
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