Prerequisites: MATH 010B with a grade of “C-” or better; MATH 031 with a grade of “C-” or better; MATH 046 or MATH 146A with a grade of “C-” or better; or consent of instructor
Description: Explores examples of dynamical systems, quadratic maps, maps of the circle, and higher-dimensional examples. Includes symbolic dynamics, Sarkovskii’s theorem, hyperbolic- ity, and structural stability. Introduces chaotic dynam- ical systems and the period doubling route to chaos. Also introduces basic notions from complex dynamics. Includes the Julia set and the Mandelbrot set.