3 citations · 6 across the 5 of their papers we have counts for
5 papers
Continued fractions and heavy sequences
Michael Boshernitzan, David Ralston
We initiate the study of the sets , , of real for which the sequence (viewed mod 1) consistently hits the interval at least as often as exp…
On the Frequency of Balanced Times in Cylinder Flows
Jon Chaika, David Ralston
Given an irrational alpha and an x in the unit interval, the set of balanced times, for which the same number of (k*alpha+x) (modulo one) are less than or equal to one half as are…
Heaviness in Toral Rotations
Yuval Peres, David Ralston
We investigate the dimension of the set of points in the d-torus which have the property that their orbit under rotation by some alpha hits a fixed closed target A more often than…
Heaviness in Symbolic Dynamics: Substitution and Sturmian Systems
David Ralston
Heaviness refers to a sequence of partial sums maintaining a certain lower bound and was recently introduced and studied in "Heaviness: and Extension of a Lemma of Y. Peres." After…
Heaviness: An Extension of a Lemma of Y. Peres
David Ralston
We provide an elementary proof of Y. Peres' lemma on the existence in certain dynamical systems of what we term heavy points, points whose ergodic averages consistently dominate th…