Have you tried mapping the Lyapunov exponent in a,b space? Years ago a professor introduced me to some really cool images created this way for the logistic map where R is replaced by a repeating sequence {A, A, B, A, etc.}. A and B are then varied over [0,4], and each value of (A, B) is mapped to an (x, y) coordinate. The value of the Lyapunov exponent is mapped from -infinity = blue (stable) through 0 = black (periodic) to red = positive (chaos).

My old physics department lore has it that this professor shared this idea with someone else, and now these carry that person’s name.

Alright I’ll be the dumbass: can someone tell me what the hell I’m looking at?

Have you tried mapping the Lyapunov exponent in a,b space? Years ago a professor introduced me to some really cool images created this way for the logistic map where R is replaced by a repeating sequence {A, A, B, A, etc.}. A and B are then varied over [0,4], and each value of (A, B) is mapped to an (x, y) coordinate. The value of the Lyapunov exponent is mapped from -infinity = blue (stable) through 0 = black (periodic) to red = positive (chaos).

My old physics department lore has it that this professor shared this idea with someone else, and now these carry that person’s name.

Jupyter notebook located at https://github.com/trislee/cool-notebooks/blob/master/Henon.ipynb