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 [bowen1979hausdorff] )

For a Kleinian group $\Gamma$, is the Hausdorff dimension of $\Lambda (\Gamma)

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?

If $\varphi _t$ is flow on a homogeneous space $G/ \Gamma$ with positive entropy, then there exists a compact $\varphi _t $ invariant section for the action of $N$ If the flow has entropy 0 and is ergodic, does this mean that there is no $N$?

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 Implications among unique ergodicity minimality entropy zero plus ergodicity Simple or semi-simple case Which one-parameter subgroups are unstable/stable foliations for some ergodic affine? Try a). Relate dynamical properties to representations of the group. K-property implies Bernoull? Weak mixing plus center s.s. implies Bernoulli? [For parts d and e, try nilmanifolds first] Ergodic implies there is a unique measure of maximal entropy?