 9441 Simo, Carles
 Averaging under Fast Quasiperiodic Forcing
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Mar 2, 94

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Abstract. We consider a non autonomous system of ordinary differential equations.
Assume that the time dependence is quasiperiodic with large basic
frequencies, $\omega /\varepsilon$ and that the $\omega$ vector
satisfies a diophantine condition. Under suitable hypothesis of
analyticity, there exists an analytic (time depending) change of
coordinates, such that the new vector field is the sum of an autonomous
part and a time dependent remainder. The remainder has an exponentially
small bound of the form $\exp(c\varepsilon^{a})$, where $c$ and $a$
are positive constants. The proof is obtained by iteration of an
averaging process. An application is made to the splitting of the
separatrices of a twodimensional normally hyperbolic torus, including
several aspects: formal approximation of the torus and their invariant
manifolds, numerical computations of the splitting, a first order
analysis using a Melnikov approach and the bifurcations of the set of
homoclinic orbits.
(This is the text of a paper delivered at the NATOASI
"Integrability and chaos in Hamiltonian systems" held
in Torun, Poland 1993)
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