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- W2147955247 abstract "We study a Hamiltonian describing a pendulum coupled with several anisochronous oscillators, giving a simple construction of unstable KAM tori and their stable and unstable manifolds for analytic perturbations. When the coupling takes place through an even trigonometric polynomial in the angle variables, we extend analytically the solutions of the equations of motion, order by order in the perturbation parameter, to a large neighbourhood of the real line representing time. Subsequently, we devise an asymptotic expansion for the splitting (matrix) associated with a homoclinic point. This expansion consists of contributions that are manifestly exponentially small in the limit of vanishing gravity, by a shift-of-contour argument. Hence, we infer a similar upper bound for the splitting itself. In particular, the derivation of the result does not call for a tree expansion with explicit cancellation mechanisms. Typeset in LTEX 2e using AMS -LTEX 2.0 and a modification of the gsm-l document class. ISBN 952-92-0338-1 (paperback) ISBN 952-10-3128-X (PDF) http://ethesis.helsinki.fi/ Otamedia Oy Espoo 2006 In memoriam Pertti Lounesto — an inspiring teacher" @default.
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- W2147955247 date "2006-05-20" @default.
- W2147955247 modified "2023-09-26" @default.
- W2147955247 title "Homoclinic Splitting without Trees" @default.
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