Chaotic Dynamical Systems

The aim of this course is to provide insight into elementary topics and current studies in the theory of chaotic dynamical systems. The focus will be on providing the students with basics in the area and introduce them to the fundamentals in this field. This course discusses the various definitions of Mathematical Chaos in elementary analytical way.

Week 1 : Analysis of the dynamics
Week 2 : Dynamics of one-dimensional maps of both the interval and the circle
Week 3 : Recurrence and minimality
Week 4 : Elementary bifurcations
Week 5 : Sarkovski’s theorem
Week 6 : Li Yorke chaos and Scrambled sets
Week 7 : ATransitivity and Devaney Chaos
Week 8 : Stronger forms of Transitivity
Week 9 : Symbolic Dynamics
Week 10 : Topological Entropy
Week 11 : Higher Dimensional Dynamics
Week 12 : Toral Automorphisms and Henon Map