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3-manifolds that admit knotted solenoids as attractors
Author(s):
Boju
Jiang;
Yi
Ni;
Shicheng
Wang
Journal:
Trans. Amer. Math. Soc.
356
(2004),
4371-4382.
MSC (2000):
Primary 57N10, 58K05, 37E99, 37D45
Posted:
February 27, 2004
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Additional information
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:
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
Posted:
February 27, 2004
Additional Notes:
This work was partially supported by a MOSTC grant and a MOEC grant
Copyright of article:
Copyright
2004,
American Mathematical Society
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