Eremenko’s Conjecture for Functions with Real Zeros: The Role of the Minimum Modulus
Eremenko’s Conjecture for Functions with Real Zeros: The Role of the Minimum Modulus
Abstract We consider the class of real transcendental entire functions $f$ of finite order with only real zeros and show that if the iterated minimum modulus tends to $\infty $, then the escaping set $I(\,f)$ of $f$ has the structure of a spider’s web, in which case Eremenko’s conjecture holds. …