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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Lyapunov graphs of nonsingular Smale flows on $ S^{1}{\times}S^{2}$


Author: Bin Yu
Journal: Trans. Amer. Math. Soc. 365 (2013), 767-783
MSC (2010): Primary 37C15, 57N10; Secondary 37D15, 37B30
Published electronically: August 22, 2012
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Abstract: In this paper, following J. Franks' work on Lyapunov graphs of nonsingular Smale flows on $ S^3$, we study Lyapunov graphs of nonsingular Smale flows on $ S^1 \times S^2$. More precisely, we determine necessary and sufficient conditions on an abstract Lyapunov graph to be associated with a nonsingular Smale flow on $ S^1 \times S^2$. We also study the singular type vertices in Lyapunov graphs of nonsingular Smale flows on 3-manifolds.


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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: http://dx.doi.org/10.1090/S0002-9947-2012-05636-4
PII: S 0002-9947(2012)05636-4
Keywords: 3-manifold, $S^{1} ×S^{2}$, nonsingular Smale flow, Lyapunov graph
Received by editor(s): March 9, 2011
Received by editor(s) in revised form: March 10, 2011
Published electronically: August 22, 2012
Additional Notes: The author was supported in part by the NSFC (grant no. 11001202).
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.