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Trudy SVMO, 2009, Volume 11, Number 2, Pages 26–34 (Mi svmo164)  

In Middle Volga Mathematical Society

$f$-adapted filtration for Morse-Smale diffeomorphisms

V. Z. Grinesa, O. V. Pochinkab, A. E. Shishenkovaa, L. A. Kuprinaa

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.

References: PDF file   HTML file
UDC: 517.956.2

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