The number of topologically non-equivalent minimal functions on closed surfaces
We consider two classes of smooth functions with three critical values on smooth closed surface of genus $g\geq1$, that possess only one (degenerate) saddle critical point in addition to $k$ local maxima and $l$ local minima. Namely: $C_{k,l}(M_g)$ is the class of such functions on oriented surface...
Збережено в:
| Дата: | 2015 |
|---|---|
| Автори та афіліації: |
|
| Ключові слова: | keywords |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Українська |
| Опубліковано: |
Інститут математики НАН України
2015
|
| Онлайн доступ: | https://trim.imath.kiev.ua/index.php/trim/article/view/135 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Transactions of Institute of Mathematics of NAS of Ukraine |
| Завантажити файл: |
|
Репозитарії
Transactions of Institute of Mathematics of NAS of Ukraine| Резюме: | We consider two classes of smooth functions with three critical values on smooth closed surface of genus $g\geq1$, that possess only one (degenerate) saddle critical point in addition to $k$ local maxima and $l$ local minima. Namely: $C_{k,l}(M_g)$ is the class of such functions on oriented surface $M_g$ and $C_{k,l}(N_g)$ -- on non-oriented surface $N_g$. In this paper we calculate the number of topologically non-equivalent (minimal) functions from the class $C_{1,1}(M_g)$ for all $g\geq 1$and from the class $C_{1,1}(N_g)$ for $g=5, 6$. Asymptotic estimate for number of topologically non-equivalent functions from the class $C_{1,1}(N_g)$ (as $g\to\infty$) are also established. |
|---|