Introducing undergraduate students to dynamical systems In my department a course on dynamical systems is offered this semester. It is a course offered to third (out of four) year undergraduate students and it involves basic dynamics of real maps, logistics map, Sharkovsky's theorem and basic dynamics of complex polynomials.
I have been asked to contribute to this course, and I was thinking about giving tasks to the students. That is, reading about topics that will not be covered in the course, but are fairly close to it and present to the whole class what they have learned and enjoyed about the topic. In this, I hope to promote cooperation and motivate them to engage in the pursuit of results beyond the course.
I know of some articles that should be suitable for undergraduates to read. Of course, under supervision and guidance. For example, this article.
So, I would like to ask, if anybody knows of any articles that offer a gentle and elementary description of dynamical phenomena of polynomials, with minimal to no prerequisites of complex analysis, much like the aforementioned one. Such articles covering other topics I mentioned above are welcome as well.
Thank you!
 A: A lot of early results of "discrete chaos" were popularized by Robert May and co-authors using population dynamics. Many of his papers are accessible to undergraduates, e.g.,

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*May, R. M. (1976). Simple mathematical models with very complicated dynamics. Nature, 261, 459-467.


*May, R. M. (1974). Biological populations with nonoverlapping generations: stable points, stable cycles, and chaos. Science, 186(4164), 645-647.


*May, R. M., & Oster, G. F. (1976). Bifurcations and dynamic complexity in simple ecological models. The American Naturalist, 110(974), 573-599.


*May, R. M. (1985). Regulation of populations with nonoverlapping generations by microparasites: a purely chaotic system. The American Naturalist, 125(4), 573-584.
And one more (very personal) things: once one of my students discovered how to produce the curves on the bifurcation diagrams. I was very excited since I had no idea that this result was known for quite a while. Here is a readable paper on this:


*Neidinger, R. D., & Annen III, R. J. (1996). The road to chaos is filled with polynomial curves. The American mathematical monthly, 103(8), 640-653.

A: I'm a fan of Chaos, Fractals and Dynamics: Computer Experiments in Mathematics by Bob Devaney. He's got a bunch of other interesting looking elementary books on dynamics too.
