All Questions

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 $\{ x_n \}$ ...

Suppose the dynamical system $(X,T)$ has only proper factors (i.e. not $(X,T)$ itself) of zero topological entropy. Does the system $(X,T)$ also have zero entropy?

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 solved many cases for the following dynamical system $\dot{x} = x (1-x-ay)$ and $\dot{y} = c y (1- b x -y)$. However, I reached the case where $c>0$ and $a>1$, $b=1$ and I ended up with the ...

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

It is a known fact [1] that, for every $c\in (1,\infty]$, it is possible to find a finite alphabet $\mathcal{A}$ and a word $w\in \mathcal{A}^\omega$ such that $w$ has critical exponent $c$. It looks ...