Math 5470 TERM PROJECT Due Tuesday, Treibergs April 26, 2016 Your Proposal is due Thurs., March 10, 2016. The term project is a short paper (of five word processor pages) or other original creative work on any topic of dynamical systems, chaos or fractal geometry related to this course. It should be a self-contained mathematical paper rather than a book report. It should be written to be readable by any student taking the course. This paper gives the student an opportunity to explore an interesting topic in more depth. It also provides a chance to practice writing. FOCUS! Since the paper is short it should develop one single idea. Formulate your main point and develop it. It could be about a theorem or a model or a method. WRITE MATHEMATICS! The paper should provide some history of the problem and motivate the results. It should include some theorems and their proofs or models and their analyses. Provide sufficiently large diagrams and tables where appropriate. Summarize and interpret the results. BE SCHOLARLY! Support your writing with attributable references, such as mathematics books and articles from mathematics journals. You should have at least three references that are books or journal articles. Internet sources should be referenced by the author and should include a complete URL. WRITE WELL! Your paper should have good technical writing style and not be chatty. You are to work alone on this project. By submitting this assignment, you are representing that it is your own work and that you have followed the rules associated with the assignment. Incidents of academic misconduct (including cheating, plagiarizing, research misconduct, misrepresenting ones own work, and/or inappropriately collaborating on an assignment) will be dealt with severely, in accordance with the Student Code (http://www.regulations.utah.edu/academics/6-400.html). A single instance of academic misconduct may result in a failing grade for the course. Multiple instances of academic misconduct may result in probation, suspension or dismissal from a program, suspension or dismissal from the University, or revocation of a degree or certificate. PREPARE A PROPOSAL. Please prepare a one paragraph paper proposal and hand it in March 10. Pick the topic you plan to write about and try to be specific about what you will say about the topic. If you have already discussed your project with me, pleasE jot down what we agreed. I would be happy to discuss your project, and to give feedback as you start writing. POSSIBLE TOPICS Some ideas for project topics can be found in the various problems we never had a chance to explore throughout the book. You can begin with the text problem and follow up on the references. You can report on the mathematics or try to add your own contributions. Here is a quick list of projects * Pattern formation in fluid systems. Raleigh-Bernard convection. Couette flow. * Ising model of magnetism * Zebra stripes and butterfly wing patterns. A biochemical switch turns on the colored pigment when a signal threshold is exceeded. * Hysteretic activation as in protien transcription. * Phosphorylation as a mechanism for4 cell reproduction. * Josephson Junction array dynamics. * How Einstein's theory changes Newtonian orbital mechanics. * Index theory on closed surfaces. * Prove existence of a closed trajectory for the generalized Lienard System. * Fitzhugh-Nagumo model of neural activity. * Spruce budworm infestations of northern Utah forests. * Hopf bifurcation in binocular vision. * Schnackenburg's model of glycolysis. * Sarkovski's theorem that period three implies chaos for maps. * Constructing fractals as fixed points of set-valued maps. * Exploring various notions of dimension as they apply to cracks.