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, hyperbolicity, and structural stability. Introduces chaotic dynamical systems and the period doubling route to chaos. Also introduces basic notions from complex dynamics. Includes the Julia set and the Mandelbrot set.