On a characteristic property of periodic entire functions

On Periodic Shadowing Property

In this paper, some properties of the periodic shadowing are presented. It is shown that a homeomorphism has the periodic shadowing property if and only if so does every lift of it to the universal covering space. Also, it is proved that continuous mappings on a compact metric space with the periodic shadowing and the average shadowing property also have the shadowing property and then are chao...

On the Arithmetical Properties of Certain Entire Characteristic Functions

A Theorem on Entire Functions

Let G(k) = ∫ 1 0 g(x)e kxdx, g ∈ L1(0, 1). The main result of this paper is the following theorem. THEOREM 1. There exists g 6≡ 0, g ∈ C∞ 0 (0, 1), such that G(kj) = 0, kj < kj+1, limj→∞ kj =∞, limk→∞ |G(k)| does not exist, lim supk→+∞ |G(k)| = ∞. This g oscillates infinitely often in any interval [1− δ, 1], however small δ > 0 is. MSC: 30D15, 42A38, 42A63

Siegel Disks and Periodic Rays of Entire Functions

Let f be an entire function whose set of singular values is bounded and suppose that f has a Siegel disk U such that f |∂U is a homeomorphism. We extend a theorem of Herman by showing that, if the rotation number of U is diophantine, then ∂U contains a critical point of f . More generally, we show that, if U is a (not necessarily diophantine) Siegel disk as above, then U is bounded. Suppose fur...

Laguerre entire functions and the Lee-Yang property

Laguerre entire functions are the polynomials of a single complex variable possessing real nonpositive zeros only or their limits on compact subsets of C. These functions are employed to establish a property of isotropic (i.e., OðNÞ-invariant) probability measures on R , N 2 N. It is called the Lee–Yang property since, in the case N 1⁄4 1, it corresponds to the property of the partition functio...