UIC Graduate Student Seminar
Friday October 26
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.