 0536 Guido Gentile, M.V. Bartuccelli, J.H.B. Deane
 Summation of divergent series and Borel summability
for strongly dissipative equations
with periodic or quasiperiodic forcing terms
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Jan 28, 05

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Abstract. We consider a class of second order ordinary differential equations
describing onedimensional systems with a quasiperiodic analytic
forcing term and in the presence of damping.
As a physical application one can think of a
resistorinductorvaractor circuit with a periodic
(or quasiperiodic) forcing function, even if the range of
applicability of the theory is much wider.
In the limit of large damping we look for quasiperiodic solutions
which have the same frequency vector of the forcing term, and we study
their analyticity properties in the inverse of the damping coefficient.
We find that already the case of periodic forcing terms is nontrivial,
as the solution is not analytic in a neighbourhood of the origin:
it turns out to be Borelsummable. In the case of
quasiperiodic forcing terms we need Renormalization Group
techniques in order to control the small divisors arising in the
perturbation series. We show the existence of a summation criterion
of the series in this case also, but, however, this
can not be interpreted as Borel summability.
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