Exponential estimates of symplectic slow manifolds

Research output: Contribution to journalJournal articleResearchpeer-review

117 Downloads (Pure)


In this paper we prove the existence of an almost invariant symplectic slow manifold for analytic Hamiltonian slow-fast systems with finitely many slow degrees of freedom for which the error field is exponentially small. We allow for infinitely many fast degrees of freedom. The method we use is motivated by a paper of MacKay from 2004. 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. We also present a stability result and obtain a generalization of a result of Gelfreich and Lerman on an invariant slow manifold to (finitely) many fast degrees of freedom.
Original languageEnglish
JournalJournal of Differential Equations
Issue number1
Number of pages46
Publication statusPublished - 2016

Fingerprint Dive into the research topics of 'Exponential estimates of symplectic slow manifolds'. Together they form a unique fingerprint.

Cite this