Realizing full n-shifts in simple Smale flows

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• 作者：Michael C. Sullivan ^{mikesullivan@math.siu.edu}
• 关键词：primary ; 37D20 ; secondary ; 37B10 ; 37D05 ; 37D45 ; 57M25
• 刊名：Topology and its Applications
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：218
• 期：Complete
• 页码：19-29
• 全文大小：385 K
• 卷排序：218

文摘

Smale flows on 3-manifolds can have invariant saddle sets that are suspensions of shifts of finite type. We look at Smale flows with chain recurrent sets consisting of an attracting closed orbit a, a repelling closed orbit r and a saddle set that is a suspension of a full n  -shift and draw some conclusions about the knotting and linking of a∪ra∪r. For example, we show for all values of n it is possible for a and r to be unknots. For any even value of n   it is possible for a∪ra∪r to be the Hopf link, a trefoil and meridian, or a figure-8 knot and meridian.