Genus two Smale-Williams solenoids in 3-manifolds

2006/10/16 by Jiming Ma, Bin Yu, Ma, Jiming +1
Mathematics · Physics and Astronomy · #37D45 #37E99 #57N10 #58K05 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.math/0610474

openalex publication_date 2006/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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