Stability of the Rotating Ellipsoidal D0-brane System

In this note we prove the complete stability of the classical fluctuation modes of the rotating ellipsoidal membrane. The analysis is carried out in the full SU(N) setting, with the conclusion that the fluctuation matrix has only positive eigenvalues. This proves that the solution will remain close to the original one for all time, under arbitrary infinitesimal perturbations of the gauge fields.Comment: 10 pages, LaTe

Distribution of periodic trajectories of Anosov C-system

The hyperbolic Anosov C-systems have a countable set of everywhere dense periodic trajectories which have been recently used to generate pseudorandom numbers. The asymptotic distribution of periodic trajectories of C-systems with periods less than a given number is well known, but a deviation of this distribution from its asymptotic behaviour is less known. Using fast algorithms, we are studying the exact distribution of periodic trajectories and their deviation from asymptotic behaviour for hyperbolic C-systems which are defined on high dimensional tori and are used for Monte-Carlo simulations. A particular C-system which we consider in this article is the one which was implemented in the MIXMAX generator of pseudorandom numbers. The generator has the best combination of speed, reasonable size of the state, and availability for implementing the parallelization and is currently available generator in the ROOT and CLHEP software packages at CERN.Comment: 22 pages, 14 figure