Accumulation points of normalized approximations

Abstract: Consider the collection of all accumulation points of normalized integer vector translates of points qα with α ∈ R^d and q ∈ Z. For each normalization factor, We find the lebesgue measure of the set of α whose accumulation points are all of R^d and of the complement set. In cases, where the lebesgue measure is zero, we seek finer information about Hausdorff dimensions of the corresponding sets.

dynamical systemsnumber theory

Audience: general audience

New England Dynamics and Number Theory Seminar