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

DOI:
https://doi.org/10.1090/S0002-9947-04-03503-2

Published electronically:
February 27, 2004

MathSciNet review:
2067124

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Abstract | References | Similar Articles | 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:
https://doi.org/10.1090/S0002-9947-04-03503-2

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