No infinite spin for partial collisions converging to isolated central configurations on the plane

2025
journal article
article
dc.abstract.enIn the n-body problem, when a cluster of bodies tends to a collision, then its normalized shape curve converges to the set of normalized central configurations, which has SO(2) symmetry in the planar case. This leaves a possibility that the normalized shape curve tends to the circle obtained by rotation of some central configuration instead of a particular point on it. This is the infinite spin problem which concerns the rotational behavior of total collision orbits in the n-body problem. The question also makes sense for partial collision. We show that the infinite spin is not possible if the limiting circle is isolated from other connected components of the set of normalized central configurations. Our approach extends the method from recent work for total collision by Moeckel and Montgomery, which was based on a combination of the center manifold theorem with Łojasiewicz inequality. To that we add a shadowing result for pseudo-orbits near normally hyperbolic manifold and careful estimates on the influence of other bodies on the cluster of colliding bodies.
dc.affiliationWydział Matematyki i Informatyki : Instytut Informatyki i Matematyki Komputerowej
dc.contributor.authorGierzkiewicz-Pieniążek, Anna - 117454
dc.contributor.authorSchaefer, Rodrigo G.
dc.contributor.authorZgliczyński, Piotr - 132902
dc.date.accession2025-07-04
dc.date.accessioned2025-07-07T10:45:54Z
dc.date.available2025-07-07T10:45:54Z
dc.date.createdat2025-07-04T07:15:05Zen
dc.date.issued2025
dc.date.openaccess0
dc.description.accesstimew momencie opublikowania
dc.description.number7
dc.description.versionostateczna wersja wydawcy
dc.description.volume406
dc.identifier.articleid158
dc.identifier.doi10.1007/s00220-025-05340-3
dc.identifier.eissn1432-0916
dc.identifier.issn0010-3616
dc.identifier.projectDRC AI
dc.identifier.urihttps://ruj.uj.edu.pl/handle/item/555162
dc.identifier.weblinkhttps://link.springer.com/article/10.1007/s00220-025-05340-3
dc.languageeng
dc.language.containereng
dc.rightsUdzielam licencji. Uznanie autorstwa 4.0 Międzynarodowa
dc.rights.licenceCC-BY
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/legalcode.pl
dc.share.typeinne
dc.subtypeArticle
dc.titleNo infinite spin for partial collisions converging to isolated central configurations on the plane
dc.title.journalCommunications in Mathematical Physics
dc.typeJournalArticle
dspace.entity.typePublicationen
dc.abstract.en
In the n-body problem, when a cluster of bodies tends to a collision, then its normalized shape curve converges to the set of normalized central configurations, which has SO(2) symmetry in the planar case. This leaves a possibility that the normalized shape curve tends to the circle obtained by rotation of some central configuration instead of a particular point on it. This is the infinite spin problem which concerns the rotational behavior of total collision orbits in the n-body problem. The question also makes sense for partial collision. We show that the infinite spin is not possible if the limiting circle is isolated from other connected components of the set of normalized central configurations. Our approach extends the method from recent work for total collision by Moeckel and Montgomery, which was based on a combination of the center manifold theorem with Łojasiewicz inequality. To that we add a shadowing result for pseudo-orbits near normally hyperbolic manifold and careful estimates on the influence of other bodies on the cluster of colliding bodies.
dc.affiliation
Wydział Matematyki i Informatyki : Instytut Informatyki i Matematyki Komputerowej
dc.contributor.author
Gierzkiewicz-Pieniążek, Anna - 117454
dc.contributor.author
Schaefer, Rodrigo G.
dc.contributor.author
Zgliczyński, Piotr - 132902
dc.date.accession
2025-07-04
dc.date.accessioned
2025-07-07T10:45:54Z
dc.date.available
2025-07-07T10:45:54Z
dc.date.createdaten
2025-07-04T07:15:05Z
dc.date.issued
2025
dc.date.openaccess
0
dc.description.accesstime
w momencie opublikowania
dc.description.number
7
dc.description.version
ostateczna wersja wydawcy
dc.description.volume
406
dc.identifier.articleid
158
dc.identifier.doi
10.1007/s00220-025-05340-3
dc.identifier.eissn
1432-0916
dc.identifier.issn
0010-3616
dc.identifier.project
DRC AI
dc.identifier.uri
https://ruj.uj.edu.pl/handle/item/555162
dc.identifier.weblink
https://link.springer.com/article/10.1007/s00220-025-05340-3
dc.language
eng
dc.language.container
eng
dc.rights
Udzielam licencji. Uznanie autorstwa 4.0 Międzynarodowa
dc.rights.licence
CC-BY
dc.rights.uri
http://creativecommons.org/licenses/by/4.0/legalcode.pl
dc.share.type
inne
dc.subtype
Article
dc.title
No infinite spin for partial collisions converging to isolated central configurations on the plane
dc.title.journal
Communications in Mathematical Physics
dc.type
JournalArticle
dspace.entity.typeen
Publication
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