Products of conjugacy classes in Chevalley groups I. Extended covering numbers

This paper is concerned with products of conjugacy classes in Chevalley groups. We prove that in any quasisimple Chevalley groupG proper or twisted, over any field, the extended covering number is bounded above linearly in terms of the rank ofG, that is, for some constante, for any Chevalley groupG, the product of anye · rank(G) non-central classes covers all ofG. We give estimates for the constante in different cases. The authors gratefully acknowledge the support of EPSRC through a Visiting Fellowship number GR/M58542 and a Research grant number GR/L92174.     

On the mixing property for hyperbolic systems

We describe an elementary argument from abstract ergodic theory that can be used to prove mixing of hyperbolic flows. We use this argument to prove the mixing property of product measures for geodesic flows on (not necessarily compact) negatively curved manifolds. We also show the mixing property for the measure of maximal entropy of a compact rank-one manifold.     

Dispersive estimates and the 2D cubic NLS equation

We prove that the initial value problem for the 2D cubic semi-linear Schrödinger equation is well-posed in the Besov space B _0, ^∞2 (?²). For this, we rely on some new dispersive inequalities derived from bilinear restriction theorems.     

The structure group of an alternative algebra

The structure group of an alternative algebra and various canonical subgroups are defined and investigated. Using the principle of triality, natural sets of generators for these groups in the case of octonion algebras are exhibited. Horst Tietz zur Vollendung des achtzigsten Lebensjahres gewidmet     

Spectral analysis and numerical simulation for second order elliptic operator with highly oscillating coefficients in perforated domains with a periodic structure

This paper discusses the spectral properties and numerical simulation for the second order elliptic operators with rapidly oscillating coefficients in the domains which may contain small cavities distributed periodically with period ε. A multiscale asymptotic analysis formula for this problem is obtained by constructing properly the boundary layer. Finally, numerical results are given, which provide a strong support for the analytical estimates     

Variational methods for the choreography solution to the three- body problem

In this paper, we give a short proof for the existence of nontrivial choreography solution to the equal-mass three-body problem, which is discovered by Chenciner and Montgomery recently.