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Every $ 3$-manifold admits a structurally stable nonsingular flow with three basic sets


Author: Bin Yu
Journal: Proc. Amer. Math. Soc. 144 (2016), 4949-4957
MSC (2010): Primary 37C15, 37D20; Secondary 57M99
DOI: https://doi.org/10.1090/proc/13122
Published electronically: May 3, 2016
MathSciNet review: 3544542
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Abstract: This paper is devoted to proving that every closed orientable $ 3$-manifold admits a simple Smale flow $ X_t$. Here a simple Smale flow is a structurally stable nonsingular flow whose chain recurrent set is composed of a periodic orbit attractor, a periodic orbit repeller and a transitive saddle invariant set, i.e., a saddle basic set.


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Additional Information

Bin Yu
Affiliation: Department of Mathematics, Tongji University, Shanghai 200092, People’s Republic of China
Email: binyu1980@gmail.com

DOI: https://doi.org/10.1090/proc/13122
Received by editor(s): September 24, 2015
Received by editor(s) in revised form: January 23, 2016
Published electronically: May 3, 2016
Communicated by: Nimish A. Shah
Article copyright: © Copyright 2016 American Mathematical Society