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Published November 2004 | Submitted + Published
Journal Article Open

3-manifolds that admit knotted solenoids as attractors

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.

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.

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Published - S0002-9947-04-03503-2.pdf

Submitted - 0403427v1.pdf

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Additional details

Created:
August 19, 2023
Modified:
October 23, 2023