4 problems

Let an inflation tiling be one-dimensional, with inflation factor a Pisot–Vijayaraghavan number and inflation matrix $M$ having an irreducible characteristic polynomial. Here, a Pi…

A substitution tiling is locally finite if, up to rigid motions, it contains only finitely many two-tile configurations. A tiling substitution has a linear expansion determined by…

Consider quadrilateral tiling billiards and their trajectories. Density property. The density property holds for quadrilateral tiling billiards. In the surrounding discussion, dens…

Sufficiency conjecture. The condition on $\phi$ in the theorem is also sufficient for $\phi$ to be an expansion map of a self-affine tiling of $\mathbb R^d$.