The Birkhoff Normal Form through the Lens of Representation Theory
We derive the simplest version of the finite-order Birkhoff normal forms [BNFs], that for area-preserving maps of the plane, using the finite-dimensional representation theory for the group of linear area-preserving maps of that plane and of its circle subgroup. We describe our motivation: the utility of understanding the 3rd-order BNF to obtain KAM stability for non-trivial periodic orbits which arise in celestial mechanics.
Authors
- Richard Murdoch Montgomery (ORCID: https://orcid.org/0009-0000-3526-2199)
Institutions
- University of California, Santa Cruz (US)
Publication Details
- Journal
- Regular and Chaotic Dynamics
- Published
- 2025-08-04
- DOI
- https://doi.org/10.1134/s1560354725520016
- Primary Topic
- Quantum chaos and dynamical systems
- Type
- article
- Field-Weighted Citation Impact
- 0.00