$f$-adapted filtration for Morse-Smale diffeomorphisms
V. Z. Grines1, L. A. Kuprina2, O. V. Pochinka3, A. E. Shishenkova4
| Annotation | We introduce the concept and prove existing of $f$-adapted filtration for Morse-Smale diffeomorphisms on manifold of diomension $n\geq 2$. It is shown that for gradient-like diffeomorphisms given on 3-manifolds, existing of minimal filtration is equivalent to almost tame embedding of separatrices of saddle periodic points. |
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| Keywords | filtration, Morse-Smale diffeomorphism, tame embedding of separatrices. |
1Professor, head of chair, Nizhny Novgorod State Agricultural Academy, Nizhny Novgorod; vgrines@yandex.ru.
2Associate professor of NGSHA, Nizhny Novgorod State Agricultural Academy, Nizhny Novgorod; math@agri.sci-nnov.ru.
3Associate professor of NNGU, Nizhny Novgorod State University, Nizhny Novgorod; olga-pochinka@yandex.ru.
4Associate professor of NGSHA, Nizhny Novgorod State Agricultural Academy, Nizhny Novgorod; math@agri.sci-nnov.ru.
Citation: V. Z. Grines, L. A. Kuprina, O. V. Pochinka, A. E. Shishenkova, "[$f$-adapted filtration for Morse-Smale diffeomorphisms]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,11:2 (2009) 26–34 (In Russian)
