The algebraic degree of coupled oscillators

Kurzanzeige
dc.contributor.authorBreiding, Paul
dc.contributor.authorMichalek, Mateusz
dc.contributor.authorMonin, Leonid
dc.contributor.authorTelen, Simon
dc.date.accessioned2025-10-28T09:41:25Z
dc.date.available2025-10-28T09:41:25Z
dc.date.issued2025-11
dc.description.abstractApproximating periodic solutions to the coupled Duffing equations amounts to solving a system of polynomial equations. The number of complex solutions measures the algebraic complexity of this approximation problem. Using the theory of Khovanskii bases, we show that this number is given by the volume of a polytope. We also show how to compute all solutions using numerical nonlinear algebra.
dc.description.versionpublisheddeu
dc.identifier.doi10.1016/j.aim.2025.110492
dc.identifier.urihttps://kops.uni-konstanz.de/handle/123456789/74993
dc.language.isoeng
dc.subjectKhovanskii bases
dc.subjectGraver bases
dc.subjectToric ideals
dc.subjectDiscriminants
dc.subjectHomotopy continuation
dc.subject.ddc510
dc.titleThe algebraic degree of coupled oscillatorseng
dc.typeJOURNAL_ARTICLE
dspace.entity.typePublication
kops.citation.bibtex
@article{Breiding2025-11algeb-74993,
  title={The algebraic degree of coupled oscillators},
  year={2025},
  doi={10.1016/j.aim.2025.110492},
  number={Part B},
  volume={480},
  issn={0001-8708},
  journal={Advances in Mathematics},
  author={Breiding, Paul and Michalek, Mateusz and Monin, Leonid and Telen, Simon},
  note={Article Number: 110492}
}
kops.citation.iso690BREIDING, Paul, Mateusz MICHALEK, Leonid MONIN, Simon TELEN, 2025. The algebraic degree of coupled oscillators. In: Advances in Mathematics. Elsevier. 2025, 480(Part B), 110492. ISSN 0001-8708. eISSN 1090-2082. Verfügbar unter: doi: 10.1016/j.aim.2025.110492deu
kops.citation.iso690BREIDING, Paul, Mateusz MICHALEK, Leonid MONIN, Simon TELEN, 2025. The algebraic degree of coupled oscillators. In: Advances in Mathematics. Elsevier. 2025, 480(Part B), 110492. ISSN 0001-8708. eISSN 1090-2082. Available under: doi: 10.1016/j.aim.2025.110492eng
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kops.sourcefieldAdvances in Mathematics. Elsevier. 2025, <b>480</b>(Part B), 110492. ISSN 0001-8708. eISSN 1090-2082. Verfügbar unter: doi: 10.1016/j.aim.2025.110492deu
kops.sourcefield.plainAdvances in Mathematics. Elsevier. 2025, 480(Part B), 110492. ISSN 0001-8708. eISSN 1090-2082. Verfügbar unter: doi: 10.1016/j.aim.2025.110492deu
kops.sourcefield.plainAdvances in Mathematics. Elsevier. 2025, 480(Part B), 110492. ISSN 0001-8708. eISSN 1090-2082. Available under: doi: 10.1016/j.aim.2025.110492eng
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source.publisherElsevier

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