4 problems

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…

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…