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Topological classification of Morse–Smale diffeomorphisms without heteroclinic curves on 3-manifolds

Published online by Cambridge University Press:  12 December 2017

CH. BONATTI ,
V. GRINES ,
F. LAUDENBACH  and
O. POCHINKA
CH. BONATTI
Affiliation:
Laboratoire de Topologie, UMR 5584 du CNRS, 2078 Dijon, France email [email protected]
V. GRINES
Affiliation:
National Research University Higher School of Economics, 603005, Nizhny Novgorod, B. Pecherskaya, 25, Russia email [email protected], [email protected]
F. LAUDENBACH
Affiliation:
Université de Nantes, LMJL, UMR 6629 du CNRS, 44322 Nantes, France email [email protected]
O. POCHINKA
Affiliation:
National Research University Higher School of Economics, 603005, Nizhny Novgorod, B. Pecherskaya, 25, Russia email [email protected], [email protected]
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Abstract

We show that, up to topological conjugation, the equivalence class of a Morse–Smale diffeomorphism without heteroclinic curves on a $3$-manifold is completely defined by an embedding of two-dimensional stable and unstable heteroclinic laminations to a characteristic space.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 9 , September 2019 , pp. 2403 - 2432
Copyright
© Cambridge University Press, 2017 

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