10 problems

Let $E_{\kappa}$ be an exponential map with a Siegel disk $U$ whose rotation number is of bounded type. The singular value is $\kappa$, and $\infty$ denotes the point at infinity i…

Infinitely many bifurcation trees conjecture. There are infinitely many bifurcation trees.

Let $E_{\kappa}(z)=e^z+\kappa$ be an exponential map, let $J(E_{\kappa})$ denote its Julia set, and let $I(E_{\kappa})$ denote its escaping set. An order-preserving conjugacy betwe…

Let $W$ be a hyperbolic component in the parameter space of exponential maps, and let $\mathcal{W}(W)$ denote its wake. A subwake of $W$ is a wake associated with a child component…

Let $E_\kappa(z)=e^z+\kappa$ be an exponential map whose singular value $\kappa$ does not escape. A repelling periodic point is a periodic point of $E_\kappa$ whose multiplier has…

Let $S$ be a spray on a manifold $M$, and let $\exp$ denote its exponential map, whose value at $p\in M$ is defined by $\exp_p(v)=c_v(1)$ whenever the geodesic $c_v$ with…

Injectivity conjecture. The $P$-adic $L$-series is non-zero if and only if the exponential map $\exp_E:L_\infty^d\rightarrow L_\infty^d$ is injective.

Let $\widetilde{Exp}_e$ be the reduced exponential map, let $\mathcal{D}$ be its domain, let $\mathcal{R}$ be its range, and let $\mathcal{C}$ and $s_{max}$ be as defined in the pa…

Let $E_\kappa\colon z\mapsto e^z+\kappa$ be an exponential map, and let $B$ be its bifurcation locus. A parameter ray is one of the curves in parameter space contained in the escap…

Let $E_\kappa\colon z\mapsto e^z+\kappa$ be an exponential map, where $\kappa$ is its unique singular value. A map is structurally stable if it is topologically conjugate to…