| Autor: |
Henryk Żołądek |
| Jazyk: |
angličtina |
| Rok vydání: |
2023 |
| Předmět: |
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| Zdroj: |
Communications in Analysis and Mechanics, Vol 15, Iss 2, Pp 300-341 (2023) |
| Druh dokumentu: |
article |
| ISSN: |
2836-3310 |
| DOI: |
10.3934/cam.2023016?viewType=HTML |
| Popis: |
We present an approach to Lyapunov theorems about a center for germs of analytic vector fields based on the Poincaré–Dulac and Birkhoff normal forms. Besides new proofs of three Lyapunov theorems, we prove their generalization: if the Poincaré–Dulac normal form indicates the existence of a family of periodic solutions, then such a family really exists. We also present new proofs of Weinstein and Moser theorems about lower bounds for the number of families of periodic solutions; here, besides the normal forms, some topological tools are used, i.e., the Poincaré–Hopf formula and the Lusternik–Schnirelmann category on weighted projective spaces. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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