Nonautonomous dynamics: classification, invariants, and implementation
| Autor: | V. Z. Grines, L. M. Lerman |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Contemporary Mathematics. Fundamental Directions. 68:596-620 |
| ISSN: | 2949-0618 2413-3639 |
| DOI: | 10.22363/2413-3639-2022-68-4-596-620 |
| Popis: | The work is a brief review of the results obtained in nonautonomous dynamics based on the concept of uniform equivalence of nonautonomous systems. This approach to the study of nonautonomous systems was proposed in [10] and further developed in the works of the second author, and recently - jointly by both authors. Such an approach seems to be fruitful and promising, since it allows one to develop a nonautonomous analogue of the theory of dynamical systems for the indicated classes of systems and give a classi cation of some natural classes of nonautonomous systems using combinatorial type invariants. We show this for classes of nonautonomous gradient-like vector elds on closed manifolds of dimensions one, two, and three. In the latter case, a new equivalence invariant appears, the wild embedding type for stable and unstable manifolds [14,17], as shown in a recent paper by the authors [5]. |
| Databáze: | OpenAIRE |
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