3-manifolds that admit knotted solenoids as attractors

2004/03/25 by Boju Jiang, Jiang, Boju, Yi Ni +3 · 1 citation
Mathematics · #37D45 #37E99 #57N10 #58K05 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #math.DS #math.GT #msc:37D45 #msc:37E99 #msc:57N10 #msc:58K05

paper · pdf · doi:10.48550/arxiv.math/0403427

16 pages, 8 figures

arxiv created 2004/03/25 · arxiv updated 2009/12/01

Abstract

Motivated by the study in Morse theory and Smale's work in dynamics, the following questions are studied and answered: (1) When does a 3-manifold admit an automorphism having a knotted Smale solenoid as an attractor? (2) When does a 3-manifold admit an automorphism whose non-wandering set consists of Smale solenoids? The result presents some intrinsic symmetries for a class of 3-manifolds.

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• Knotting Minimal Sets

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