Normal stability of slow manifolds in nearly periodic Hamiltonian systems
No Thumbnail Available
Access rights
openAccess
URL
Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
This publication is imported from Aalto University research portal.
View publication in the Research portal (opens in new window)
View/Open full text file from the Research portal (opens in new window)
Other link related to publication (opens in new window)
View publication in the Research portal (opens in new window)
View/Open full text file from the Research portal (opens in new window)
Other link related to publication (opens in new window)
Authors
Date
2021-09-01
Department
Major/Subject
Mcode
Degree programme
Language
en
Pages
27
Series
Journal of Mathematical Physics, Volume 62, issue 9
Abstract
Kruskal [J. Math. Phys. 3, 806 (1962)] showed that each nearly periodic dynamical system admits a formal U(1) symmetry, generated by the so-called roto-rate. We prove that such systems also admit nearly invariant manifolds of each order, near which rapid oscillations are suppressed. We study the nonlinear normal stability of these slow manifolds for nearly periodic Hamiltonian systems on barely symplectic manifolds—manifolds equipped with closed, non-degenerate 2-forms that may be degenerate to leading order. In particular, we establish a sufficient condition for long-term normal stability based on second derivatives of the well-known adiabatic invariant. We use these results to investigate the problem of embedding guiding center dynamics of a magnetized charged particle as a slow manifold in a nearly periodic system. We prove that one previous embedding and two new embeddings enjoy long-term normal stability and thereby strengthen the theoretical justification for these models.Description
Funding Information: The work of J.W.B. was supported by the Los Alamos National Laboratory LDRD program under Project No. 20180756PRD4. The work of E.H. was supported by the Academy of Finland (Grant No. 315278). Any subjective views or opinions expressed herein do not necessarily represent the views of the Academy of Finland or Aalto University. Publisher Copyright: © 2021 Author(s).
Keywords
Other note
Citation
Burby, J W & Hirvijoki, E 2021, ' Normal stability of slow manifolds in nearly periodic Hamiltonian systems ', Journal of Mathematical Physics, vol. 62, no. 9, 093506 . https://doi.org/10.1063/5.0054323