Transcendental dynamics explores the iteration of entire functions, whose complex analytic nature leads to richly varied behaviours distinct from those observed in rational maps. In this context, ...

In the theory of analytic characteristic functions (c.f.'s), it is well-known that: (1) the order of an entire c.f. cannot be less than unity, unless the function is identically equal to one (P. Lévy) ...

Let $f(z_1,\ldots,z_n)$ be an entire function of the $n(\geqq 2)$ complex variables $z_1,\ldots,z_n$ holomorphic for $|z_t| \leqq r_t, t = 1,\ldots n$. We have ...