The Basics of Maps - Chaos Theory | Lecture 1

We begin this lecture series on chaos theory with a broad introduction to discrete-time dynamical systems. Focusing on one-dimensional mappings, we define fundamental concepts such as orbits, fixed points, periodic points, and stable and unstable manifolds. We explore the geometric interpretations of orbits, providing intuition for how points move under iteration and how the system’s structure shapes long-term behavior. The lecture concludes with a discussion of maps on the circle, setting the stage for more advanced topics in the lectures that follow and building a foundation for understanding the emergence of complex and chaotic dynamics. Learn how to draw a cobweb diagram:    • Cobweb Diagrams - Math Modelling | Lecture 14   More information on the instructor: https://hybrid.concordia.ca/jbrambur/ Follow @jbramburger7 on Twitter for updates.