Normal forms for strong magnetic systems on surfaces

• Verfasst von: Asselle, Luca [VerfasserIn]
• Verfasst von: Benedetti, Gabriele [VerfasserIn]
• Titel: Normal forms for strong magnetic systems on surfaces
• Titelzusatz: trapping regions and rigidity of Zoll systems
• Verf.angabe: Luca Asselle and Gabriele Benedetti
• E-Jahr: 2022
• Jahr: June 2022
• Umfang: 27 S.
• Fussnoten: "Published online by Cambridge University Press: 22 March 2021". - Artikel-Frontdoor ; Gesehen am 20.06.2024
• Titel Quelle: Enthalten in: Ergodic theory and dynamical systems
• Ort Quelle: Cambridge, Mass. : Cambridge Univ. Press, 1981
• Jahr Quelle: 2022
• Band/Heft Quelle: 42(2022), 6 vom: Juni, Seite 1871-1897
• ISSN Quelle: 1469-4417
• DOI: doi:10.1017/etds.2021.11
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: 37C55
• Sach-SW: 58E10
• Sach-SW: 70H08
• Sach-SW: 70H11
• Sach-SW: 70H12
• Sach-SW: 70H14
• Sach-SW: invariant tori
• Sach-SW: KAM theory
• Sach-SW: magnetic flows
• Sach-SW: Zoll systems
• K10plus-PPN: 1891941615
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

We prove a normal form for strong magnetic fields on a closed, oriented surface and use it to derive two dynamical results for the associated flow. First, we show the existence of invariant tori and trapping regions provided a natural non-resonance condition holds. Second, we prove that the flow cannot be Zoll unless (i) the Riemannian metric has constant curvature and the magnetic function is constant, or (ii) the magnetic function vanishes and the metric is Zoll. We complement the second result by exhibiting an exotic magnetic field on a flat two-torus yielding a Zoll flow for arbitrarily weak rescalings.