3-manifolds that admit knotted solenoids as attractors

Jiang, Boju; Ni, Yi; Wang, Shicheng

doi:10.1090/S0002-9947-04-03503-2

3-manifolds that admit knotted solenoids as attractors
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by Boju Jiang, Yi Ni and Shicheng Wang PDF

Trans. Amer. Math. Soc. 356 (2004), 4371-4382 Request permission

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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