Continued fractions and heavy sequences (2009)
Boshernitzan, Michael, Ralston, David
We initiate the study of the sets $H(c)$, $00$, then $x\in H_m$ if and only if $y\in \hat H_m$. The motivation for the present study comes from Y. Peres's ergodic lemma.
On the Frequency of Balanced Times in Cylinder Flows (2009)
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 larger than one...
Controlled Divergence of Discrepancy Sums (2009)
Answering an informal question of K. Park, we show that by fixing some irrational alpha to have a particular standard continued fraction expansion, we may force the associated discrepancy sequences...
Heaviness: An Extension of a Lemma of Y. Peres (2009)
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 the expected value of...
Heaviness in Symbolic Dynamics: Substitution and Sturmian Systems (2009)
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 a review of basic...
Heaviness in Circle Rotations (2009)
We are concerned with describing the structure of the set of points in the unit interval which, when subjected to rotation by irrational alpha modulo one, for all finite portions of the orbit contain...
Heaviness in Toral Rotations (2009)
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 expected for all...
Heaviness: An extension of a lemma of Yuval Peres (2008)
Ralston, David, Ralston, David
In a 1988 paper, Y. Peres proved that in any probability-measure preserving system {X, mu, T}, where X is compact and T is continuous, coupled with a continuous function f, there is at least one...
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Four tigers and the dragon: values differences, similarities, and consensus
Ho-Beng Chia, Carolyn Egri, David Ralston, Ping Fu, Min-Hsun Kuo, Chay-Hoon Lee, ...
This study examines the influence of economic and political factors that contribute to the convergence and/or divergence in value priorities of five East Asian societies—China, Hong Kong,...