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In 1988, Mayer proved the remarkable fact that $$\infty $$ ∞ is an explosion point for the set $$E(f_a)$$ E ( f a ) of endpoints of the Julia set of $$f_a:\mathbb {C}\rightarrow \mathbb {C}; \mathrm{e}^z+a$$ f a : C → C ; e z + a with $$a<-1$$ a < - 1 ; that is, the set $$E(f_a)$$ E ( f a ) is totally separated (in particular, it...