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.
INTENDED AUDIENCE :Researchers, Senior undergraduates, Post graduates
PREREQUISITES : A good course in Real Analysis, Metric Spaces.l
INDUSTRY SUPPORT : None
COURSE LAYOUTWeek 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