Geometric theory of unimodular Pisot substitutions

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Topological Properties of Rauzy Fractals (2010, background): “This story can be revisited in the framework of hyperbolic attractors as detailed in [30]: from the considerations in [17, 31, 127] it follows that every orientable hyperbolic one-dimensional attractor is either a substitution tiling space or a classical solenoid.”
On the Pisot Substitution Conjecture (2015, background): “[65, 30] Let φ be a primitive Pisot substitution that is also unimodular and irreducible.”
Tilings associated with beta-numeration and substitutions. (2005, background): “• Spectral theory [ BK04 , Sie04]: the lattice multiple tiling is a tiling if and only if the substitutive dynamical system (Xσ ,S ) has a purely discrete spectrum.”