Quasi-reversible instabilities of closed orbits
Identifieur interne : 000060 ( France/Analysis ); précédent : 000059; suivant : 000061Quasi-reversible instabilities of closed orbits
Auteurs : M. G. Clerc [Chili, États-Unis] ; P. Coullet [France] ; N. Vandenberghe [France] ; E. Tirapegui [Chili]Source :
- Physics Letters A [ 0375-9601 ] ; 2001.
Abstract
We characterize the three generic quasi-reversible instabilities of closed orbits: the quasi-reversible saddle-node, the Krein collision and the period doubling bifurcation. We show that after a periodic change of variables the asymptotic normal forms of the last two instabilities are the Maxwell–Bloch and the Lorenz equations. We exhibit a simple example of the quasi-reversible period doubling bifurcation, the quasi-reversible 2:1 resonance.
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DOI: 10.1016/S0375-9601(01)00490-X
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Física, Univ. de Chile, Casilla 487-3, Santiago</wicri:regionArea><wicri:noRegion>Santiago</wicri:noRegion></affiliation></author></analytic><monogr></monogr><series><title level="j">Physics Letters A</title><title level="j" type="abbrev">PLA</title><idno type="ISSN">0375-9601</idno><imprint><publisher>ELSEVIER</publisher><date type="published" when="2001">2001</date><biblScope unit="volume">287</biblScope><biblScope unit="issue">3–4</biblScope><biblScope unit="page" from="198">198</biblScope><biblScope unit="page" to="204">204</biblScope></imprint><idno type="ISSN">0375-9601</idno></series><idno type="istex">BE625E734B64C31E6F44F43B20683786150085BB</idno><idno type="DOI">10.1016/S0375-9601(01)00490-X</idno><idno type="PII">S0375-9601(01)00490-X</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0375-9601</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">We characterize the three generic quasi-reversible instabilities of closed orbits: the quasi-reversible saddle-node, the Krein collision and the period doubling bifurcation. We show that after a periodic change of variables the asymptotic normal forms of the last two instabilities are the Maxwell–Bloch and the Lorenz equations. We exhibit a simple example of the quasi-reversible period doubling bifurcation, the quasi-reversible 2:1 resonance.</div></front></TEI><affiliations><list><country><li>Chili</li><li>France</li><li>États-Unis</li></country><region><li>Provence-Alpes-Côte d'Azur</li></region><settlement><li>Valbonne</li></settlement></list><tree><country name="Chili"><noRegion><name sortKey="Clerc, M G" sort="Clerc, M G" uniqKey="Clerc M" first="M. G." last="Clerc">M. G. Clerc</name></noRegion><name sortKey="Tirapegui, E" sort="Tirapegui, E" uniqKey="Tirapegui E" first="E." last="Tirapegui">E. Tirapegui</name></country><country name="États-Unis"><noRegion><name sortKey="Clerc, M G" sort="Clerc, M G" uniqKey="Clerc M" first="M. G." last="Clerc">M. G. 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