Continual Version of the Perron Effect of Change in Values of Characteristic Exponents
- Авторлар: Izobov N.1, Il’in A.2
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Мекемелер:
- Institute of Mathematics
- Faculty of Computational Mathematics and Cybernetics
- Шығарылым: Том 97, № 1 (2018)
- Беттер: 52-57
- Бөлім: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/225456
- DOI: https://doi.org/10.1134/S1064562418010180
- ID: 225456
Дәйексөз келтіру
Аннотация
A nonlinear perturbed differential system with a linear approximation is considered. An open question has been the validity of a (continual) version of the Perron effect when the set of Lyapunov exponents of all nontrivial solutions (necessarily infinitely extendable on the right) of the corresponding nonlinear perturbed system with a perturbation of arbitrary higher order of smallness in a neighborhood of the origin is measurable, lies entirely on the positive half-line, and has the cardinality of the continuum and even a positive Lebesgue measure. The positive answer to this question is given by the presented theorem, which generally determines an explicit representation of the Lyapunov exponents of all nontrivial solutions to the nonlinear system in terms of their initial values.
Авторлар туралы
N. Izobov
Institute of Mathematics
Хат алмасуға жауапты Автор.
Email: izobov@im.bas-net.by
Белоруссия, Minsk
A. Il’in
Faculty of Computational Mathematics and Cybernetics
Email: izobov@im.bas-net.by
Ресей, Moscow, 119992