4 problems

Limit-set conjecture. Under the assumptions of Theorem $$ , for almost every $\xi\in\mathcal{X}$, the $\omega$-limit set $\omega(\xi)$ is given by either a fixed point, a limit cyc…

Let $G_{6,3}=\langle a_0,\cdots,a_5\mid a_i^3=id,\ a_ia_{i+1}=a_{i+1}a_i,\ i\in\mathbb{Z}/6\mathbb{Z}\rangle$ be the hyperbolic group with boundary the Menger curve, and let…

Cannon–Thurston conjecture. The inclusion $\tilde{i}:\widetilde{S^h}\rightarrow\mathbb{H}^3$ extends continuously to the boundary.

Let $a=\zeta_k$ and $x=\zeta_m$ be primitive roots of unity, with $m\geq3$. Limit-point conjecture. The continued fraction $K_a(x)$ converges exactly when … and hence exactly when…