ABSTRACT
THE PINBALL MACHINE is one of those rare dynamical systems whose chaotic nature we can deduce by pure qualitative reasoning, with fair confidence that we have not wandered astray. Nevertheless, the angles in the paths of the balls that are introduced whenever a ball strikes a pin and rebounds-rather prominent features of Figure 1-render the system somewhat inconvenient for detailed quantitative study. For an everyday system that will vary more smoothly, and can more easily serve to illustrate many of the basic properties of chaotic behavior, even though it may not yield so readily to descriptive arguments, let us consider one that still bears some resemblance to the pinball machine. The new system will again be a slope, with a ball or some other object rolling or sliding down it, but there will be no pins or other obstacles to block a smooth descent, and the slope may be of any size.
