MATH 303
Introduction to Dynamics, p-Adics, and Measure Fall 2021
Division III Quantative/Formal Reasoning
This is not the current course catalog

At its most basic level a dynamical system consists of a set of points and a transformation or map acting on the set (i.e., sending points in the set to other points in the set). In this setting we can already ask about the existence, and prevalence, of periodic points (points that come back to themselves). One can also ask about the orbit of a point: the set of points that is obtained as one iteratively applies the transformation the point. An important dynamical notion that comes up here is that of chaos. The course will start by studying basic dynamical systems using notions from calculus. Then we will introduce the p-adic numbers and use them to study dynamical systems. The course will end with an exploration of the notion of measure and its connection with dynamical systems.