Finite Codimension Stability of Invariant Surfaces
Abstract Following recent work of Alazard and Shao [AlSh] on applications of para-differential calculus to smooth conjugacy and stability problems for Hamiltonian systems, we prove finite codimension stability of invariant surfaces (in finite differentiability classes) of flat geodesic flows on translation surfaces. The result is also based on work of the author [F97, F21] on the cohomological equation for translation flows.
Authors
- Giovanni Forni (ORCID: https://orcid.org/0000-0002-6777-986X)
Institutions
- CY Cergy Paris Université (FR)
- Analyse, Géométrie et Modélisation (FR)
- University of Maryland, College Park (US)
Publication Details
- Journal
- Communications in Mathematical Physics
- Published
- 2026-10-26
- DOI
- https://doi.org/10.1007/s00220-026-05764-5
- Primary Topic
- Mathematical Dynamics and Fractals
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Science Foundation
- European Commission
- European Research Council