Asymptotic sequences

Asymptotic Behavior of Moment Sequences

In this paper we study asymptotic behavior of some moment spaces. We consider two different settings. In the first one, we work with ordinary multi-dimensional moments on the standard m-simplex. In the second one, we deal with the trigonometric moments on the unit circle of the complex plane. We state large and moderate deviation principles for uniformly distributed moments. In both cases the r...

The Asymptotic Density of Sequences

Asymptotic Behavior of Certain Ducci Sequences Asymptotic Behavior of Certain Ducci Sequences

The Ducci map applied to vectors in R is considered. It is shown that for any starting vector, the corresponding sequence of iterates either eventually becomes periodic or, if not eventually periodic, asymptotically approaches the zero vector. A precise characterization of which vectors exhibit each of these separate behaviors is given.

Asymptotic Geometry of Non-mixing Sequences

The exact order of mixing for zero-dimensional algebraic dynamical systems is not entirely understood. Here non-Archimedean norms in function fields of positive characteristic are used to exhibit an asymptotic shape in non-mixing sequences for algebraic Z-actions. This gives a relationship between the order of mixing and the convex hull of the defining polynomial. Using these methods, we show t...

Asymptotic Behavior of Certain Ducci Sequences

The Ducci map is considered applied to vectors in R. It is shown that for certain starting vectors of odd length, the corresponding sequence of iterates asymptotically approaches a periodic vector, but never becomes periodic itself. On the other hand, for any starting vectors not of this type, it is shown that the corresponding Ducci sequence becomes eventually periodic. A simple method for det...