CHAOTIC DYNAMICAL SYSTEMS
A presentation by Victor J. Donnay, Associate Professor of Mathematics, Bryn Mawr College, and students and colleagues at the College
In Dynamical Systems, an object moves according to a rule. Depending on the
rule motion, the object may move in a regular fashion or in a chaotic
fashion. We illustrate the ideas of chaos theory by letting the user play
with three different types of dynamical systems:
1. Billiards in which a ball moves around inside a billiard table.
The user can choose different shapes for the table (polygon, circle,
ellipse, stadium). For some shapes, the billiard motion is regular; for
others it is chaotic.
2. The Phase Space Game in which a point hops around inside a
rectangle. The moving point produces beautiful colored patterns. The user
can vary the rules of motion to produce either a regular pattern, a
chaotic pattern or a pattern that has a mixture of regular and chaotic
behaviour.
3. Iteration of a point on the real number line. A point moves on
the number line according to various rules that the user chooses. One can
display the motion either numerically or using the staircase method.
Java Applets by:
 Derya Davis, Mathematics and Physics, Bryn Mawr College
 Stadium Billiards, Circle Billiards
 Carin Ewing, Philosophy, Bryn Mawr College
 Polygonal Billiards, Standard Map, Iteration Applet
 Zhenjian He, Computer Science and Mathematics, Bryn Mawr College
 Elliptic Billiards
 Tina Shen, Computer Science, Bryn Mawr College
 Polygonal Billiards, Staircase Game
Advisors:
 Bogdan Butoi, Graduate Student in Mathematics, Bryn Mawr College
 Victor Donnay, Associate Professor of Mathematics, Bryn Mawr College
 Deepak Kumar, Assistant Professor of Computer Science, Bryn Mawr College
Supported in part by a grant to the College from the Howard Hughes Medical Institute.
Send any comments to:
vdonnay@brynmawr.edu

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