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

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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.## References

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## Additional Information

**Bin Yu**- Affiliation: Department of Mathematics, Tongji University, Shanghai 200092, People’s Republic of China
- MR Author ID: 823461
- Email: binyu1980@gmail.com
- 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
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**144**(2016), 4949-4957 - MSC (2010): Primary 37C15, 37D20; Secondary 57M99
- DOI: https://doi.org/10.1090/proc/13122
- MathSciNet review: 3544542