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3-manifolds that admit knotted solenoids as attractors

Jiang, Boju and Ni, Yi and Wang, Shicheng (2004) 3-manifolds that admit knotted solenoids as attractors. Transactions of the American Mathematical Society, 356 (11). pp. 4371-4382. ISSN 0002-9947.

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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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Additional Information:© 2004 American Mathematical Society. Received by the editors February 20, 2003 and, in revised form, April 18, 2003. This work was partially supported by a MOSTC grant and a MOEC grant. We would like to thank the referee for his suggestions which enhanced the paper. We also thank Professors H. Duan, S. Gan and L. Wen for helpful conversations.
Funding AgencyGrant Number
Subject Keywords:3-manifolds, homeomorphisms, attractors, solenoids, lens spaces
Issue or Number:11
Classification Code:2000 Mathematics Subject Classification. Primary 57N10, 58K05, 37E99, 37D45
Record Number:CaltechAUTHORS:20150421-115923758
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:56832
Deposited By: George Porter
Deposited On:21 Apr 2015 19:38
Last Modified:03 Oct 2019 08:17

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