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Period 3 Implies Chaos - Dynamical Systems | Lecture 32

In this lecture we learn about one of the most famous results in all of chaos theory: "Period 3 Implies Chaos." This incredible result is due to Li and Yorke and was published in 1975. In fact, it is the first occurrence of the word chaos in the mathematics literature to describe the complex dynamics that can arise in discrete-time dynamical systems. In this lecture we state and prove the "Period 3 Theorem." Interestingly, one needs little more than basic calculus to arrive at the result. Towards the end of the lecture I also present the Sharkovskii Theorem, which is a generalization of Li and Yorke's result. Read the original paper yourself: https://www.jstor.org/stable/2318254 This course is taught by Jason Bramburger for Concordia University. More information on the instructor: https://hybrid.concordia.ca/jbrambur/ Follow @jbramburger7 on Twitter for updates.