EQUIDISTRIBUTION OF SPARSE SEQUENCES ON NILMANIFOLDS

作者：Frantzikinakis Nikos^*

来源：Journal d Analyse Mathematique, 2009, 109(1): 353-395.

DOI：10.1007/s11854-009-0035-y

We study equidistribution properties of nil-orbits (b(n) x)(n is an element of N) when the parameter n is restricted to the range of some sparse sequence that is not necessarily polynomial. For example, we show that if X = G/Gamma a nilmanifold, b is an element of G is an ergodic nilrotation, and c is an element of R \ Z is positive, then the sequence (b([n c])x)(n is an element of N) is equidistributed in X for every x is an element of X. This is also the case when n(c) is replaced with a(n), where a(t) is a function that belongs to some Hardy field, has polynomial growth, and stays logarithmically away from polynomials, and when it is replaced with a random sequence of integers with sub-exponential growth. Similar results have been established by Boshernitzan when X is the circle.

• 出版日期2009-10