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Regular version of the site

Article

О градиентно-подобных потоках на локально-тривиальных расслоениях

Динамические системы. 2015. Т. 5. № 1-2. С. 25-30.
Гуревич Е. Я., Зинина С. Х.

We obtain  topological classification of  3 dimensional manifolds admitting gradient - like flows whose non-wandering set belongs to  attracting and repelling closed  invariant  surfaces. We show that such manifolds are mapping tori (that are factor spaces of direct product of a surface  $\mathbb{S}_g $ and the interval  $[0,1]$ via  equivalence relation $(z,1)\sim (\tau,0)$, where  $\tau\colon \mathbb{S}_g\to \mathbb{S}_g$ is a homeomorphism). We obtain sufficient conditions for  $\tau$  to be isotopic to periodic map.