An important mathematical discovery of the 20th century is
that
simple nonlinear deterministic dynamical systems can exhibit apparently
random dynamical behavior. This discovery will be illustrated using
the simple dynamical system that changes the state <i>X</i>, a real number in
the
unit interval, to the new state <i>4X(1-X)</i>. For example, I will show the
following remarkable result: Given any sequence of ``heads'' and
``tails''
produced by tossing a coin, there is a state which, under repeated
iteration
of the process, visits the subintervals <i>H=[0,1/2]</i> and <i>T=[1/2,1]</i> in the
specified sequential order of <i>H</i>'s and <i>T</i>'s. To understand my talk, all
you
need to know is how to compose two functions, some basic trigonometry,
and the meaning of the decimal representation of a real number.


Dr. Chicone is a  Professor of Mathematics at the University of
Missouri, Columbia.
 He works
in the area of dynamical systems.

 Afterwards Dr. Chicone will talk about graduate study opportunities at the University of Missouri.