Let f : C → C be an entire map of the form f(z) = P (z) exp(Q(z)), where P and Q are polynomials of arbitrary degrees (we allow the case Q = 0). Building upon a method pioneered by M. Shishikura, we show that if f has a Siegel disk of bounded type rotation number centered at the origin, then the boundary of this Siegel disk is a quasicircle containing at least one critical point of f . This uni...

The principal term in the asymptotic expansion of the variance of the periodic measure of a ball in R under uniform random shift is proportional to the (d + 1)st power of the grid scaling factor. This result remains valid for a bounded set in R with sufficiently smooth isotropic covariogram under a uniform random shift and an isotropic rotation, and the asymptotic term is proportional also to t...

Abstract. The goal of this paper is to describe in mathematical terms the effect on the ocean circulation of a random stationary wind stress at the surface of the ocean. In order to avoid singular behaviour, non-resonance hypotheses are introduced, which ensure that the time frequencies of the wind-stress are different from that of the Earth rotation. We prove a convergence result for a three-d...

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...

This paper deals with the problem∆u= g onG and ∂u/∂n+u f = L on ∂G. Here,G⊂ Rm, m> 2, is a bounded domain with Lyapunov boundary, f is a bounded nonnegative function on the boundary of G, L is a bounded linear functional onW1,2(G) representable by a real measure μ on the boundary of G, and g ∈ L2(G)∩Lp(G), p > m/2. It is shown that a weak solution of this problem is bounded in G if and only if ...

The nanostructures under rotation have high promising future to be used in nano-machines, nano-motors and nano-turbines. They are also one of the topics of interests and it is new in designing of rotating nano-systems. In this paper, the scale-dependent vibration analysis of a nanoplate with consideration of the axial force due to the rotation has been investigated. The governing equation and b...