Neanaliticheskie pervye integraly analiticheskikh sistem differentsial'nykh uravneniy v okrestnosti ustoychivykh polozheniy ravnovesiya
- Authors: Kozlov V.V1
-
Affiliations:
- Steklov Mathematical Institute of the Russian Academy of Sciences
- Issue: Vol 59, No 6 (2023)
- Pages: 843-846
- Section: Articles
- URL: https://journals.rcsi.science/0374-0641/article/view/144973
- DOI: https://doi.org/10.31857/S0374064123060134
- EDN: https://elibrary.ru/FIKMPW
- ID: 144973
Cite item
Abstract
In even-dimensional phase spaces, we give examples of analytic systems of differential equations that have isolated equilibria and admit nonanalytic first integrals. These integrals are positive definite in a neighborhood of the equilibria, which proves the stability of the equilibria (on the entire time axis). However, such systems of differential equations do not admit nontrivial first integrals in the form of formal power series at all. In particular, the Lyapunov stability of equilibria of analytic systems does not imply their formal stability. In the case of an odd-dimensional phase space, all isolated equilibria are apparently unstable.
About the authors
V. V Kozlov
Steklov Mathematical Institute of the Russian Academy of Sciences
Author for correspondence.
Email: kozlov@pran.ru
Moscow, 119991, Russia
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