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$f$-adapted filtration for Morse-Smale diffeomorphisms

V. Z. Grines1, L. A. Kuprina2, O. V. Pochinka3, A. E. Shishenkova4

AnnotationWe 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.
Keywordsfiltration, 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)