complex-analysis

Introduction to complex dynamics

taught

Iterating an analytic function on itself and sorting the plane into the points whose orbits stay bounded (the filled Julia set) and the ones that escape.

Taught in

An introduction to complex dynamics
Complex Analysis
Julia sets and the Mandelbrot set, qualitatively
Complex Analysis

Requires

mobius-transformations required
recursive-sequence-fixed-points helpful
Classifying a fixed point as attracting or repelling by the size of a derivative is the same idea used there for real recursive sequences, now applied to iterating an analytic map on C.

Required by

Nothing in the catalog needs this yet.

Local knowledge map

Click to expand

Solid arrows are required prerequisites; dashed are recommended or helpful. Lower rows are more foundational. Click any box to jump to that concept.