Geometry and chaos near resonant equilibria of 3-DOF Hamiltonian systems
Identifieur interne : 000672 ( Main/Exploration ); précédent : 000671; suivant : 000673Geometry and chaos near resonant equilibria of 3-DOF Hamiltonian systems
Auteurs : George Haller [États-Unis] ; Stephen Wiggins [États-Unis]Source :
- Physica D: Nonlinear Phenomena [ 0167-2789 ] ; 1996.
Abstract
In this paper we study the dynamics near resonant elliptic equilibria in three-degree-of-freedom Hamiltonian systems. The resonances we consider have multiplicity two, and the corresponding local normal form for the equilibrium is integrable at cubic order. We prove the existence of families of 3-tori and whiskered 2-tori with nearby chaotic dynamics in the quartic normal form. The whiskers of the 2-tori intersect in a non-trivial way giving rise to multi-pulse homoclinic and heteroclinic connections. These connections survive in the full system as orbits homoclinic to invariant 3-spheres.
Url:
DOI: 10.1016/0167-2789(95)00247-2
Affiliations:
Links toward previous steps (curation, corpus...)
Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title>Geometry and chaos near resonant equilibria of 3-DOF Hamiltonian systems</title>
<author><name sortKey="Haller, George" sort="Haller, George" uniqKey="Haller G" first="George" last="Haller">George Haller</name>
</author>
<author><name sortKey="Wiggins, Stephen" sort="Wiggins, Stephen" uniqKey="Wiggins S" first="Stephen" last="Wiggins">Stephen Wiggins</name>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">ISTEX</idno>
<idno type="RBID">ISTEX:D1F6C2B5F8DAE67FCC90276FBB00D5F0230C14A9</idno>
<date when="1996" year="1996">1996</date>
<idno type="doi">10.1016/0167-2789(95)00247-2</idno>
<idno type="url">https://api.istex.fr/document/D1F6C2B5F8DAE67FCC90276FBB00D5F0230C14A9/fulltext/pdf</idno>
<idno type="wicri:Area/Main/Corpus">000625</idno>
<idno type="wicri:Area/Main/Curation">000625</idno>
<idno type="wicri:Area/Main/Exploration">000672</idno>
<idno type="wicri:explorRef" wicri:stream="Main" wicri:step="Exploration">000672</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title level="a">Geometry and chaos near resonant equilibria of 3-DOF Hamiltonian systems</title>
<author><name sortKey="Haller, George" sort="Haller, George" uniqKey="Haller G" first="George" last="Haller">George Haller</name>
<affiliation wicri:level="4"><country xml:lang="fr">États-Unis</country>
<wicri:regionArea>Divison of Applied Mathematics, Box F, Brown University, Providence, RI 02912</wicri:regionArea>
<orgName type="university">Université Brown</orgName>
<placeName><settlement type="city">Providence (Rhode Island)</settlement>
<region type="state">Rhode Island</region>
</placeName>
</affiliation>
<affiliation></affiliation>
</author>
<author><name sortKey="Wiggins, Stephen" sort="Wiggins, Stephen" uniqKey="Wiggins S" first="Stephen" last="Wiggins">Stephen Wiggins</name>
<affiliation wicri:level="1"><country xml:lang="fr">États-Unis</country>
<wicri:regionArea>Department of Applied Mechanics and Control and Dynamical Systems 104-44, Caltech, Pasadena, CA 91125</wicri:regionArea>
<wicri:noRegion>CA 91125</wicri:noRegion>
</affiliation>
<affiliation></affiliation>
</author>
</analytic>
<monogr></monogr>
<series><title level="j">Physica D: Nonlinear Phenomena</title>
<title level="j" type="abbrev">PHYSD</title>
<idno type="ISSN">0167-2789</idno>
<imprint><publisher>ELSEVIER</publisher>
<date type="published" when="1996">1996</date>
<biblScope unit="volume">90</biblScope>
<biblScope unit="issue">4</biblScope>
<biblScope unit="page" from="319">319</biblScope>
<biblScope unit="page" to="365">365</biblScope>
</imprint>
<idno type="ISSN">0167-2789</idno>
</series>
<idno type="istex">D1F6C2B5F8DAE67FCC90276FBB00D5F0230C14A9</idno>
<idno type="DOI">10.1016/0167-2789(95)00247-2</idno>
<idno type="PII">0167-2789(95)00247-2</idno>
</biblStruct>
</sourceDesc>
<seriesStmt><idno type="ISSN">0167-2789</idno>
</seriesStmt>
</fileDesc>
<profileDesc><textClass></textClass>
<langUsage><language ident="en">en</language>
</langUsage>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en">In this paper we study the dynamics near resonant elliptic equilibria in three-degree-of-freedom Hamiltonian systems. The resonances we consider have multiplicity two, and the corresponding local normal form for the equilibrium is integrable at cubic order. We prove the existence of families of 3-tori and whiskered 2-tori with nearby chaotic dynamics in the quartic normal form. The whiskers of the 2-tori intersect in a non-trivial way giving rise to multi-pulse homoclinic and heteroclinic connections. These connections survive in the full system as orbits homoclinic to invariant 3-spheres.</div>
</front>
</TEI>
<affiliations><list><country><li>États-Unis</li>
</country>
<region><li>Rhode Island</li>
</region>
<settlement><li>Providence (Rhode Island)</li>
</settlement>
<orgName><li>Université Brown</li>
</orgName>
</list>
<tree><country name="États-Unis"><region name="Rhode Island"><name sortKey="Haller, George" sort="Haller, George" uniqKey="Haller G" first="George" last="Haller">George Haller</name>
</region>
<name sortKey="Wiggins, Stephen" sort="Wiggins, Stephen" uniqKey="Wiggins S" first="Stephen" last="Wiggins">Stephen Wiggins</name>
</country>
</tree>
</affiliations>
</record>
Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Amerique/explor/CaltechV1/Data/Main/Exploration
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000672 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 000672 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien |wiki= Wicri/Amerique |area= CaltechV1 |flux= Main |étape= Exploration |type= RBID |clé= ISTEX:D1F6C2B5F8DAE67FCC90276FBB00D5F0230C14A9 |texte= Geometry and chaos near resonant equilibria of 3-DOF Hamiltonian systems }}
This area was generated with Dilib version V0.6.32. |