Journal article

Publication year: 2022

Pages: 1871-1897

Journal: Ergodic Theory and Dynamical Systems

Volume number: 42

Issue number: 6

ISSN: 0143-3857

eISSN: 1469-4417

Open access status: Hybrid

DOI Link: https://doi.org/10.1017/etds.2021.11

Publisher: Cambridge University Press

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.

Harvard Citation style: Asselle, L. and Benedetti, G. (2022) Normal forms for strong magnetic systems on surfaces: trapping regions and rigidity of Zoll systems, Ergodic Theory and Dynamical Systems, 42(6), Article PII S0143385721000110. pp. 1871-1897. https://doi.org/10.1017/etds.2021.11

APA Citation style: Asselle, L., & Benedetti, G. (2022). Normal forms for strong magnetic systems on surfaces: trapping regions and rigidity of Zoll systems. Ergodic Theory and Dynamical Systems. 42(6), Article PII S0143385721000110, 1871-1897. https://doi.org/10.1017/etds.2021.11