Convergence of the Birkhoff normal form sometimes implies convergence of a normalizing transformation
2022 (English)In: Ergodic Theory and Dynamical Systems, ISSN 0143-3857, E-ISSN 1469-4417, Vol. 42, no 3, p. 1166-1187Article in journal (Refereed) Published
Abstract [en]
Consider an analytic Hamiltonian system near its analytic invariant torus T-0 carrying zero frequency. We assume that the Birkhoff normal form of the Hamiltonian at T-0 is convergent and has a particular form: it is an analytic function of its non-degenerate quadratic part. We prove that in this case there is an analytic canonical transformation-not just a formal power series-bringing the Hamiltonian into its Birkhoff normal form.
Place, publisher, year, edition, pages
Cambridge University Press (CUP) , 2022. Vol. 42, no 3, p. 1166-1187
Keywords [en]
nearly integrable Hamiltonian systems, Birkhoff normal form, convergence of the normalizing transformations
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:kth:diva-309059DOI: 10.1017/etds.2021.71ISI: 000750488900012Scopus ID: 2-s2.0-85112391799OAI: oai:DiVA.org:kth-309059DiVA, id: diva2:1639351
Note
QC 20220221
2022-02-212022-02-212022-06-25Bibliographically approved