An arithmetic remark on entire periodic functions

The Arithmetic of Entire Functions under Composition

In this paper, we prove, among other things, that any family of nonconstant entire functions of one complex variable has a greatest common right factor under composition. We prove a corresponding result for any family of pairwise dependent entire functions of N complex variables. Since f and af +b, where a, b # C and a{0 have all the same properties from the point of view of factoring under com...

1965i a Remark on an Arithmetic Theorem of Chevalley

Remark on periodic solutions of nonlinear oscillators

AppIied Mathematics Letters ~w.el~vier.ni/~ocate/~l Abstract-we contribute to the method of trigonometric series for solving differential equations of certain nonlinear oscillators.

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...

Remark about Heat Diffusion on Periodic Spaces

Let M be a complete Riemannian manifold with a free cocompact Z-action. Let k(t, m1, m2) be the heat kernel on M . We compute the asymptotics of k(t, m1, m2) in the limit in which t → ∞ and d(m1, m2) ∼ √ t. We show that in this limit, the heat diffusion is governed by an effective Euclidean metric on R coming from the Hodge inner product on H(M/Z;R).