Cobweb plots for the logistic map: a Geogebra applet

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…

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…