Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, January 4, 2005.

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Questions regarding events or the calendar should be directed to Tori Corkery.
    December 2004           January 2005          February 2005
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1  2  3  4                      1          1  2  3  4  5
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Tuesday, January 4, 2005

3:00 pm in 347 Altgeld Hall ,Tuesday, January 4, 2005

#### Unique ergodicity for nonstationary adic transformations

###### Albert Meads Fisher (University of Sao Paulo, Brazil)

Abstract: Vershik's adic transformations are generalizations of the odometer (or adding machine) transformation, but with the combinatorics of a nonstationary subshift of finite type. They are analogous to horocycle flows, and can be used to model substitution dynamical systems, circle rotations and interval exchange transformations. We give a necessary and sufficient condition for adic transformations to be uniquely ergodic. We describe a specific example, developed with Sebastien Firenczi, of a (3 X 3) adic transformation which the combinatorics of imitates Keane's famous interval exchange counterexample, and so is minimal but not uniquely ergodic.