High-School Level Introduction to Dynamical Systems

I would look at the following items.

Books:

• "A First Course In Chaotic Dynamical Systems: Theory And Experiment (Studies in Nonlinearity)" by Robert L. Devaney

• National Academy of Sciences: Science At The Frontier

• Nonlinear Dynamics and Chaos by Strogatz has a few dynamical systems on Celestial Dynamics (see problems 6.5.7 through 6.5.10), but I am not sure they are appropriate.

• It would be great if you can build an electronic circuit, analyze it with mathematics and then measure stuff with DMMs and O'scopes and the like. maybe the Van Der Pol Oscillator or a Harmonic Oscillator.

Web Sites:

• The Dynamical Systems and Technology Project at Boston University

• Discrete Dynamical Systems

• Drexel University Math Forum - for school kids

Talking about celestial mechanics, please see this pedagogical blurb: http://www.whydomath.org/node/space/index.html

I would be hard pressed to find a more spectacular success of the dynamical systems theory in the real-world.

I'd talk about the chaos game for generating images of IFS fractals or Julia sets. See the books Fractals Everywhere and Fractals for the Classroom for instance.