3 problems

Let $(X,\mathbb{Z})$ be a dynamical system generated by a homeomorphism $T:X\longrightarrow X$. The system is free when no nonzero power of $T$ has a fixed point, and it has the ma…

Zero mean dimension conjecture. Every aperiodic dynamical system with zero mean dimension has the marker property.

A free dynamical system is a topological dynamical system $(X,T)$ in which $T^n x\neq x$ for every $x\in X$ and every nonzero integer $n$. Its mean dimension is the dynamical dimen…