Regular level sets of Lyapunov graphs ofnonsingular Smale flows on 3-manifolds

Bin Yu

doi:10.3934/dcds.2011.29.1277

Article Contents

2011, Volume 29, Issue 3: 1277-1290. Doi: 10.3934/dcds.2011.29.1277

This issue Previous Article The $C^{\alpha}$ regularity of weak solutions of ultraparabolic equations Next Article Coupled-expanding maps under small perturbations

Regular level sets of Lyapunov graphs of nonsingular Smale flows on 3-manifolds

Bin Yu^1,

1.
Department of Mathematics, Tongji University, Shanghai 200092

Received: March 2010

Revised: June 2010

Published: September 2011

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Abstract

In this paper, we first discuss the regular level set of a nonsingular Smale flow (NSF) on a 3-manifold. The main result about this topic is that a 3-manifold $M$ admits an NSF which has a regular level set homeomorphic to $(n+1)T^{2}$ $(n\in \mathbb{Z}, n\geq 0)$ if and only if $M=M'$#$n S^{1}\times S^{2}$. Then we discuss how to realize a template as a basic set of an NSF on a 3-manifold. We focus on the connection between the genus of the template $T$ and the topological structure of the realizing 3-manifold $M$.

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Mathematics Subject Classification: Primary: 37D15, 37D20, 37E99; Secondary: 57N10.

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