The  Weizmann  Institute  of  Science
                  Faculty of Mathematics and Computer Science
             Geometric Functional Analysis and Probability Seminar
                    Seminar Room, Room 261, Ziskind Building
                         on Thursday, December 16, 2010
                                 11:00 - 13:00
                                 David Ralston
                             Ben Gurion University
                                 will speak on
                     Growth rates and one-sided boundedness
                          of a particular ergodic sum
Using nothing more sophisticated than first-return maps and elementary
properties of continued fractions, we will develop a constructive approach to
studying the sequence of ergodic sums of the characteristic function of the
interval $[0,1/2]$ under an irrational rotation of the circle minus the
 function of $(1/2,1)$, to ensure zero mean. The principle benefit of the
elementary (but somewhat tedious) approach is that statements may be derived
about specific rotations, as opposed to generic ones.  Our primary topics of
investigation will be:
-What growth rates are allowed for such sequences?
-What is the structure of the set of positions whose ergodic sums are
 always nonnegative?
In both cases we will develop specific examples. Time permitting, we will then
discuss applications of these techniques to informal questions of K. Park and
W. Veech, as well as ongoing work regarding dynamics on a particular infinite
translation surface (joint work with Barak Weiss of Ben Guiron University).
Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <> 
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