Abstract We prove the existence of small amplitude, time-quasi-periodic solutions (invariant tori) for incompressible Navier–Stokes equation on d -dimensional torus $$\mathbb T^d$$ T d , with a small, quasi-periodic in time external force. also show that they are orbita...

A plate periodically bonded with piezoelectric patches on its surfaces is considered. The differential quadrature element method is used to solve the wave motion equation for the two-dimensional periodic structure. The method is very simple and easy to implement. Based on the method, band structures for in-plane wave propagating in the periodic piezoelectric plate are studied, from which the fr...

we present a new renormalization-group calculation of the octagonal tiling excitation spectrum. Two new self-;imilar octagonal tilings are introduced, a triangle-Lite and a triangle-dan tiling, which are entangled with the standard rhombus-~quare tiling. The decimation procedure involved in the renormalization group calculation transforms each tiling enta a different one and goe; back tu the (r...

In this paper we construct two models for the motion of a particle under the gravitational attraction of Sun, Jupiter, Saturn and Uranus, that can be seen as a generalization of the well known Restricted Three-Body Problem (RTBP). Both models are obtained by computing quasi-periodic solutions – with two basic frequencies – of a suitable N-body problem. The first model is based on a quasi-period...

We calculate within a Bose-Hubbard tight-binding model the matter-wave flow driven by a constant force through a Bose-Einstein condensate of Rb atoms in various types of quasi-onedimensional arrays of potential wells. Interference patterns are obtained when beam splitting is induced by creating energy minigaps either through period doubling or through quasi-periodicity governed by the Fibonacci...

This paper concerns with the reducibility loss of (periodic) invariant curves of quasi-periodically forced one dimensional maps and its relationship with the renormalization operator. Let gα be a one-parametric family of one dimensional maps with a cascade of period doubling bifurcations. Between each of these bifurcations, there exists a parameter value αn such that gαn has a superstable perio...