The Persistence of a Slow Manifold with Bifurcation

Publication: Research - peer-reviewJournal article – Annual report year: 2012

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his paper considers the persistence of a slow manifold with bifurcation in a slow-fast two degree of freedom Hamiltonian system. In particular, we consider a system with a supercritical pitchfork bifurcation in the fast space which is unfolded by the slow coordinate. The model system is motivated by tethered satellites. It is shown that an almost full measure subset of a neighborhood of the slow manifold's normally elliptic branches persists in an adiabatic sense. We prove this using averaging and a blow-up near the bifurcation.


Original languageEnglish
JournalS I A M Journal on Applied Dynamical Systems
Volume11
Issue number2
Pages (from-to)661-683
ISSN1536-0040
DOIs
StatePublished - 2012
Peer-reviewedYes

Bibliographical note

Read More: http://epubs.siam.org/action/showAbstract?page=661&volume=11&issue=2&journalCode=sjaday

CitationsWeb of Science® Times Cited: 1

Keywords

  • Singularly perturbed Hamiltonian systems, Slow manifolds with bifurcations, Pitchfork bifurcations, Blow-up, Tethered satellites
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