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On the growth of the number of non-compact heteroclinic curves

НазваниеOn the growth of the number of non-compact heteroclinic curves
АвторыV. Grines1, E. Gurevich1, O. Pochinka1, A. Shilovskaya2
1National Research University Higher School of Economics
2Lobachevskii State University
АннотацияWe consider a class $SD(M^3)$ of gradient-like diffeomorphisms on closed 3-manifolds $M^3$ that have surface dynamics. In~\cite{GrGuPo-rhd} it was proven that the ambient manifold $M^3$ for such diffeomorphisms is a mapping torus $M_{g,\tau}$, $g\geq 0$, and the number of non-compact heteroclinic curves is no less than $12g$. In this paper it is established that for any integer $n\geq 12g$ there exists a mapping torus $M_{g,\tau(n)}$ and a diffeomorphism from the class $SD(M_{g,\tau(n)})$ having exactly $n$ heteroclinic curves.
Ключевые словаHeteroclinic curve, gradient-like diffeomorphism, mapping torus
Образец ссылки на статьюGrines V., Gurevich E., Pochinka O., Shilovskaya A. On the growth of the number of non-compact heteroclinic curves [Электронный ресурс] // Дифференциальные уравнения и их приложения в математическом моделировании: материалы XIII Международной научной конференции. (Саранск, 12-16 июля 2017 г.). - Саранск: СВМО, 2017. - С. 398-402. Режим доступа: http://conf.svmo.ru/files/deamm2017/papers/paper56.pdf. - Дата обращения: 19.11.2018.