DescriptionThe field of low dimensional dynamical systems is vast and the methods are taken from many different areas like Analysis, Linear Algebra, Topology and Ordinary Differential Equations. Our dynamical systems will be mainly discrete and will be given by some kind of iterations. Explicit examples are mathematical billiards, circle maps, Smale's horseshoe map, toral automorphisms, quadratic maps.The idea of this project is to first study together different aspects in the field. Very good introductions into various aspects are the books "Chaotic Dynamical Systems" by Robert Devaney and "Introduction to Dynamical Systems" by Brin and Stuck. We will also consult other sources at the right level of exposition, like Serge Tabachnikov's "Geometry of Billiards" or Lind's and Marcus' book "Symbolic Dynamics and Coding". I would expect that all participants in this project read and present material from these books to the others. Equipped with some background knowlegde at the end of the Michaelmas term, participants of this project will then branch out into different more specific topics of their own. The final reports should then cover some general overview material over dynamical systems in their first part, followed by investigations into the more specific topics studied in the second term. Some Resources
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