Exponential estimates of slow manifolds

Publication: Research - peer-reviewJournal article – Annual report year: 2013

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In this paper we prove exponential estimates of slow manifolds in analytic systems. The results are obtained for general slow-fast systems and finite-dimensional Hamiltonian systems. For general systems we consider the motion in a Banach space with an unbounded fast vector-field, while for Hamiltonian systems we consider finitely many fast and slow variables. We will prove some conjectures of MacKay from a 2004 reference, and the methods we use are based upon the ideas presented in this paper. The method does not notice resonances, and therefore we do not pose any restrictions on the motion normal to the slow manifold other than it being fast and analytic.
Original languageEnglish
JournalNonlinearity
Publication date2013
Number of pages31
StateSubmitted
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