In this lecture, I explore fixed points of dynamical systems on the line, which are also called steady-states, equilibria, or rest-states, depending on the context. I introduce the fundamental concepts of fixed points and explain what it means for them to be stable, drawing on both geometric intuition from the previous lecture and analytic criteria for rigorously determining stability. We also investigate what happens in cases where the usual stability criterion is indeterminate, showing how to approach these subtler situations. This lecture provides a clear foundation for understanding the core building blocks of dynamical behavior and sets the stage for more complex dynamics in higher dimensions.
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.
