On the closure $\overline T$ of Teichmüller space, consider a continuous parametrization $\overline T \times \Sigma_A^+ \to \mathbb S^2$ such that Image ($t, \Sigma_A^+ = \Lambda(\Gamma_t)$). Is the Hausdorff dimension of $\Lambda(\Gamma_t)$ continuous in $t \in \overline T$?
(Note, this problem was added by the editor to the end of Rufus' last paper [1])
For a Kleinian group $\Gamma$, is the Hausdorff dimension of $\Lambda (\Gamma) <2$ if $\Lambda(\Gamma)$ is not the whole sphere?
(Note, this problem was added by the editor to the end of Rufus' last paper [1])
Is $GR (\alpha) $ an algebraic integer for an automorphism $\alpha$ of solvable group?
Same setting [as question 140]. Is the $GR$ (of $g$ on $\Gamma$) an algebraic number?
Let $g : G/\Gamma \to G/\Gamma $ come from an automorphism $g$ of $G$. Is the entropy minimal in its homotopy class? Is entropy a complete invariant for automorphisms of infranilmanifolds?
Calculate $h_\mu $ for $G/\Gamma $ finite measure, non compact.
(Thom) Look at Markov partitions on $\mathbb{T}^n$ when all $\lambda_i $ are distinct and real.
Embed automorphisms of compact groups as basic sets.
This problem is not clearly legible, but it is thought to say
Unique ergodicity in Lie groups. Case with finite area instead of compact homogeneous spaces
If a translation by a group element on $G/\Gamma$ is minimal, is that element nilpotent in $\mathfrak G ?$ (i.e. has 0 entropy)
Covering space for $\Sigma_A \to \mathbb{T}^2$ corresponding to $\mathbb{R}^2 \to \mathbb{T}^2$
Entropy of automorphisms in algebra (groups, rings).
In Parry's `Conjugate to linear' paper, what are the properties of the constructed measure? Does this work for equilibrium states too?
Entropy of automorphisms of $C^\ast $-algebras
Ergodic non hyperbolic automorphisms of $\mathbb{T}^n$. Are they quotients of subshifts of finite type? Do they satisfy specification?
Homogenous dynamics
