V. Z. Grines, O. V. Pochinka, A. E. Shishenkova, L. A. Kuprina, “<nobr>$f$</nobr>-adapted filtration for Morse-Smale diffeomorphisms”, Trudy SVMO, 2009, Volume 11, Number 2,Pages <nobr>26

In Middle Volga Mathematical Society

$f$-adapted filtration for Morse-Smale diffeomorphisms

V. Z. Grines^a, O. V. Pochinka^b, A. E. Shishenkova^a, L. A. Kuprina^a

^a Nizhnii Novgorod State Agricultural Academy
^b N. I. Lobachevski State University of Nizhni Novgorod

Abstract: 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.

Keywords: filtration, Morse-Smale diffeomorphism, tame embedding of separatrices.

UDC: 517.956.2