3 problems

For a smooth dynamical system, the scalar cohomological equation is the equation obtained by taking a smooth observable and a smooth coboundary; a system is $C^\infty$-effective, o…

Let $T$ be a $C^\infty$ diffeomorphism of the torus ${\mathbb T}^d$. Assume that $T$ is topologically conjugate to the linear translation $T_\omega:{\bf x}\mapsto {\bf x}+\omega$ m…

Let $\sigma$ be an irreducible Pisot unimodular substitution, and let $\sigma^\omega$ denote its associated directive sequence. The property of being good is the property asserted…