Lyapunov graphs of nonsingular Smale flows on 𝑆¹×𝑆²

Yu, Bin

doi:10.1090/S0002-9947-2012-05636-4

Lyapunov graphs of nonsingular Smale flows on $S^{1}\times S^{2}$
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Trans. Amer. Math. Soc. 365 (2013), 767-783 Request permission

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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