## UIC Graduate Student Seminar

Friday October 26

3:00 pm

636 SEO

Speaker: Shmuel Friedland

Title: Fractals and Chaos

Abstract: In this lecture for the general public I introduce several
topics in Ergodic Theory and Dynamical Systems,
which arise in Mathematics, Physics and Engineering.
I plan to cover the following topics:

a. Three examples: Cantor set, Sierpiski's gasket and Koch's curve.

b. Iterated Function System (IFS)

c. The box and Hausdorff dimension (HD), Hausdorff measure.

Moran's formula for HD for certain IFS.

d. Period-doubling bifurcation and Feigenbaum's constant.

e. Three implies Chaos: Sharkovski's theorem.

f. Entropy, Lyapunov exponents and L.S. Young's formula for HD. (If time permits.