# Jerusalem Mathematics Colloquium

Thursday, 11th March 2004, 4:00 pm

Mathematics Building, Lecture Hall 2

##

Professor Hillel Furstenberg

(Hebrew University)

"The Dynamics of {(3/2)^n mod 1}"

** Abstract: **
Ideas from dynamics have had a certain degree of success in
problems of diophantine approximation. After a brief discussion of
some successes, we shall discuss a "dynamical" approach a longstanding
open question: Does |(3/2)^n-m|<\epsilon have a solution in natural
numbers m,n? (Of course, you can replace 3/2 by any p/q>1.)

We will be led to a variety of topics: cellular automata, Hausdorff
dimension, algebraic functions over finite fields, intersection of
"nice" fractals, etc.

The lecture will pose many problems and provide few solutions.

Light refreshments will be served in the faculty lounge at 3:30.

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