|
ИСТИНА |
Войти в систему Регистрация |
ИСТИНА ИНХС РАН |
||
Local and Global ODEs Propertiesтезисы доклада
- Авторы: Edneral V.F., Romanovski V.G.
- Сборник: http://compalg.jinr.ru/Dubna2018/abstracts2018_files/1315_Edneral.pdf
- Тезисы
- Год издания: 2018
- Аннотация: We consider autonomous planar systems of ordinary differential equations with a polynomial nonlinearity. These systems are resolved with respect to derivatives and can contain free parameters. To study local integrability of the system near each stationary points, we use an approach based on Power Geometry and on the computation of the resonant normal form. For the pair of concrete planar systems, we found the complete set of necessary conditions on parameters of the system for which the system is locally integrable near each stationary points. The main idea of this report is in the hypothesis that if for the fixed set of parameters, such that at all stationary points of the system this system is locally integrable then this system has the global first integral of motion. So from some finite set of local properties, we can obtain a global property. But if the system has some invariant lines or separatists, this first integral can exist only in the part of the phase space, where the local integrable points take place.
- Добавил в систему: Еднерал Виктор Федорович