Normalization flow in the presence of a resonance
- Authors: Treschev D.V.1
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Affiliations:
- Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
- Issue: Vol 89, No 1 (2025)
- Pages: 184-207
- Section: Articles
- URL: https://bakhtiniada.ru/1607-0046/article/view/303941
- DOI: https://doi.org/10.4213/im9595
- ID: 303941
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Abstract
Following [18], we develop an approach to the Hamiltonian theory of normal forms based on continuous averaging. We concentrate on the case of normal forms near an elliptic singular point, but unlike [18] we do not assume that frequences of the linearized system are non-resonant. We study analytic properties of the normalization procedure. In particular, we show that in the case of a codimension one resonance an analytic Hamiltonian function may be reduced to a normal form up to an exponentially small reminder with explicit estimates of the reminder and the analyticity domain.
About the authors
Dmitry Valerevich Treschev
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
Author for correspondence.
Email: treschev@mi-ras.ru
Doctor of physico-mathematical sciences, Professor
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