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Motivated by the study in Morse theory and Smale's work in dynamics, thefollowing questions are studied and answered: (1) When does a 3-manifold admitan automorphism having a knotted Smale solenoid as an attractor? (2) When doesa 3-manifold admit an automorphism whose non-wandering set consists of Smalesolenoids? The result presents some intrinsic symmetries for a class of3-manifolds.

3-manifolds that admit knotted solenoids as attractors