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| In this talk we will focus on the use of the so-called
jet transport technique to compute normal forms around
periodic orbits of ordinary differential equations (ODEs).
Jet transport is a technique to compute high order
differentials of a given numerical algorithm, with respect
to initial data and/or parameters. Combining this
method with a numerical integrator for ODEs allows to
compute Taylor expansions of Poincar\'e maps at a given
fixed point. From this power expansion it is not difficult
to compute the normal form at this point. Hence, this
allows to compute high order approximations to the
invariant manifolds around a given periodic orbit. We note
that this approach can be used in situations that are
far from integrable. |
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