All Questions

Does anyone know of a construction of a subshift (over $\mathbb{Z}$) which is (1) minimal (2) zero (topological) entropy (3) measure-theoretically strong mixing (for some measure)? I am in particular ...

I have been trying to read the paper, Topological invariants fo substitution tiling and their associated $C^*$-algebras, to learn more about a construction of Anderson-Putnam complexes. However, it ...

Let $\mathcal{M}$ the Mandelbrot set, $\mathcal{M}=\{c \in \mathbb{C}: \{Q_c^n(0) \}_{n \in \mathbb{N}} \text{ is bounded, where } Q_c(z)=z^2+c \}$ And let the hyperbolic or stable component, $H_n=\{ ...

Are SFTs uniquely ergodic in general, or is there a known necessary and sufficient condition for them to be uniquely ergodic?

$\DeclareMathOperator\Aut{Aut}$Let $X$ and $Y$ be two subshifts of finite type and $X\subset Y$, and $\phi:X\rightarrow X$ be a homeomorphism commuting with the shift map. Is there any homeomorphism $\...

Consider $f:[0,2\pi) \to [0,2\pi )$ given by $f(x) = (x + 1) \bmod 2\pi$ for all $x\in [0,2\pi )$, i.e. a shift map on the unit circle with anti-clockwise shift of $1$. Denote the sequence $\{ x_n \}$ ...