A few days ago I posted Geogebra applets illustrating discrete dynamical systems. I was using these in a differential equations lecture that I gave. In the next lecture I showed the students how to draw cobweb plots for 1-dimensional discrete dynamical systems. A discrete dynamical system is a function in which the range is a…

# Tag: chaos

## Sharkovsky’s theorem

In this post I would like to share one of the most surprising, remarkable, and beautiful results in the study of discrete dynamical systems. It relates to an unusual ordering of the positive integers: First, some definitions. The basic object of study in a discrete dynamical system is the orbit. Let be a function from…

## Fractals on NOVA

I was shocked yesterday afternoon. I turned on the television to see what was on for my kids (PBS, of course) only to see, not Bob the Builder or Word World, but the Cantor set being constructed right before my eyes. It turned out that it was a new NOVA special called Hunting the Hidden…