It is known that, for many transcendental entire functions in the Eremenko-Lyubich class $\mathcal{ B}$, every escaping point can eventually be connected to infinity by a curve of escaping points. When this is the case, we say that the functions are criniferous. In this paper, we extend this result to a new class of maps in $\mathcal{ B}$. Furthermore, we show that if a map belongs to this class, then its Julia set contains a Cantor bouquet; in other words, it is a subset of $\mathbb{ C}$ ambiently homeomorphic to a straight brush.
Categories: math.DS math.CV