4 problems

Smooth Markov partition conjecture. The induced toral endomorphism $f$ admits a smooth, in fact linear, Markov partition if and only if for some $k\in\mathbb{N}$, $A^k$ is diagonal…

Let $\Phi$ be a pseudo-Anosov flow, let $\mathcal{P}$ be its bifoliated plane, and let $\mathcal{R}$ be a Markovian family for $\Phi$. A reduced Markov partition of $\Phi$ is a Mar…

Let $d \ge 3$, let $(X,f)$ be an $\mathcal{S}$-adic mapping family satisfying the Pisot condition from Definition, and suppose that $(X,f)$ admits a nonstationary Markov partition…

Let $\mathcal{P}_0$ be the toroidal partition associated with the Jeandel–Rao Wang shift, let $\Gamma_0$ be the corresponding lattice, and let $R_0$ denote the associated…