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.References
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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
- 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
- © Copyright 2004 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 356 (2004), 4371-4382
- MSC (2000): Primary 57N10, 58K05, 37E99, 37D45
- DOI: https://doi.org/10.1090/S0002-9947-04-03503-2
- MathSciNet review: 2067124