Abstract
Using alternating Heegaard diagrams, we construct some 3-manifolds which admit diffeomorphisms such that the non-wandering sets of the diffeomorphisms are composed of Smale–Williams solenoid attractors and repellers. An interesting example is the truncated-cube space. In addition, we prove that if the nonwandering set of the diffeomorphism consists of genus two Smale–Williams solenoids, then the Heegaard genus of the closed manifold is at most two.
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