Source:http://linkedlifedata.com/resource/pubmed/id/12088053
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| Predicate | Object |
|---|---|
| rdf:type | |
| lifeskim:mentions | |
| pubmed:dateCreated |
2002-6-28
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| pubmed:abstractText |
We study orbits in potentials with central cusps, emphasizing the spheroidal equidensity (SED) potentials generated by mass distributions with spheroidal equidensity surfaces. The most prominent bifurcations are those related to 1:1 and 4:3 resonances between radial motions and motions perpendicular to the central plane. We find that 1:1 resonances can cause the thin tube orbit, as well as the equatorial plane orbit, to become unstable. We concentrate on period-tripling bifurcations because they appear to be the least understood. We study them via a class of analytic maps. This study suggests that stable period-three orbits generally arise de novo in stable and unstable pairs via a turning-point bifurcation, and not through a bifurcation from the thin tube at a 120 degree rotation angle. The stable period-three orbits typically have only a short span of existence before becoming unstable to a period-doubling instability through a supercritical pitchfork bifurcation.
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| pubmed:language |
eng
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| pubmed:journal | |
| pubmed:status |
PubMed-not-MEDLINE
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| pubmed:month |
Dec
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| pubmed:issn |
0077-8923
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| pubmed:author | |
| pubmed:issnType |
Print
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| pubmed:day |
30
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| pubmed:volume |
867
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| pubmed:owner |
NLM
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| pubmed:authorsComplete |
Y
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| pubmed:pagination |
61-84
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| pubmed:dateRevised |
2003-11-3
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| pubmed:year |
1998
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| pubmed:articleTitle |
Bifurcations of periodic orbits in axisymmetric scalefree potentials.
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| pubmed:affiliation |
Department of Mathematics, Florida State University, Tallahassee 32306-4510, USA.
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| pubmed:publicationType |
Journal Article
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