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Stable periodic solutions of periodic systems of differential equations. / Vasil’eva, E. V. .
в: Vestnik St. Petersburg University: Mathematics, Том 51, № 1, 2018, стр. 9 - 14.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Stable periodic solutions of periodic systems of differential equations
AU - Vasil’eva, E. V.
N1 - Vasil’eva, E.V. Stable Periodic Solutions of Periodic Systems of Differential Equations. Vestnik St.Petersb. Univ.Math. 51, 9–14 (2018). https://doi.org/10.3103/S1063454118010119
PY - 2018
Y1 - 2018
N2 - An infinitely differentiable periodic two-dimensional system of differential equations is considered. It is assumed that there is a hyperbolic periodic solution and there exists a homoclinic solution to the periodic solution. It is shown that, for a certain type of tangency of the stable manifold and unstable manifold, any neighborhood of the nontransversal homoclinic solution contains a countable set of stable periodic solutions such that their characteristic exponents are separated from zero.
AB - An infinitely differentiable periodic two-dimensional system of differential equations is considered. It is assumed that there is a hyperbolic periodic solution and there exists a homoclinic solution to the periodic solution. It is shown that, for a certain type of tangency of the stable manifold and unstable manifold, any neighborhood of the nontransversal homoclinic solution contains a countable set of stable periodic solutions such that their characteristic exponents are separated from zero.
KW - периодические системы
KW - устойчивые периодические решения
KW - гомоклиническая точка
UR - https://link.springer.com/article/10.3103/S1063454118010119
M3 - Article
VL - 51
SP - 9
EP - 14
JO - Vestnik St. Petersburg University: Mathematics
JF - Vestnik St. Petersburg University: Mathematics
SN - 1063-4541
IS - 1
ER -
ID: 37739450