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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

3-manifolds that admit knotted solenoids as attractors


Authors: Boju Jiang, Yi Ni and Shicheng Wang
Translated by:
Journal: Trans. Amer. Math. Soc. 356 (2004), 4371-4382
MSC (2000): Primary 57N10, 58K05, 37E99, 37D45
Published electronically: February 27, 2004
MathSciNet review: 2067124
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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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Additional Information

Boju Jiang
Affiliation: Department of Mathematics, Peking University, Beijing 100871, People’s Republic of China
Email: jiangbj@math.pku.edu.cn

Yi Ni
Affiliation: Department of Mathematics, Peking University, Beijing 100871, People’s Republic of China
Address at time of publication: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
Email: yni@princeton.edu

Shicheng Wang
Affiliation: Department of Mathematics, Peking University, Beijing 100871, People’s Republic of China
Email: wangsc@math.pku.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9947-04-03503-2
PII: S 0002-9947(04)03503-2
Keywords: $3$-manifolds, homeomorphisms, attractors, solenoids, lens spaces
Received by editor(s): February 20, 2003
Received by editor(s) in revised form: April 18, 2003
Published electronically: February 27, 2004
Additional Notes: This work was partially supported by a MOSTC grant and a MOEC grant
Article copyright: © Copyright 2004 American Mathematical Society