Normal forms for strong magnetic systems on surfaces: trapping regions and rigidity of Zoll systems
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 can...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
June 2022
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| In: |
Ergodic theory and dynamical systems
Year: 2022, Volume: 42, Issue: 6, Pages: 1871-1897 |
| ISSN: | 1469-4417 |
| DOI: | 10.1017/etds.2021.11 |
| Online Access: | Verlag, kostenfrei, Volltext: https://doi.org/10.1017/etds.2021.11 Verlag, kostenfrei, Volltext: https://www.cambridge.org/core/journals/ergodic-theory-and-dynamical-systems/article/normal-forms-for-strong-magnetic-systems-on-surfaces-trapping-regions-and-rigidity-of-zoll-systems/448C0346E502473B6A1C1374E58BA2C1# 
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| Author Notes: | Luca Asselle and Gabriele Benedetti |
| Summary: | 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. |
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| Item Description: | "Published online by Cambridge University Press: 22 March 2021". - Artikel-Frontdoor Gesehen am 20.06.2024 |
| Physical Description: | Online Resource |
| ISSN: | 1469-4417 |
| DOI: | 10.1017/etds.2021.11 |