For slightly more technical treatment, Strogatz's Nonlinear Dynamics and Chaos is now a standard text. It isn't terribly technical and is quite well written and (in my view) easy to read for anyone with a background in vector calculus, diff eqs, & perhaps a little bit of linear algebra. (There are now other good options to, some more mathematical and some more application-oriented, but I still think Strogatz is a good place to start.)

is a good modern book on it.

It is a fun problem because it stems from continuous diff eq but the answers come from topological analysis around the fixed sets, and the ways fixed sets can change as continuous parameters change.

* Exploring Chaos: Theory and Experiment by Brian Davies

* Chaos: From Theory to Applications by A.A. Tsonis

* Chaos and Fractals: An Elementary Introduction by David Feldman

* Nonlinear Dynamics And Chaos by Tufillaro, Abbott, Reilly

* Computers, pattern, chaos, and beauty: Graphics from an unseen world by Clifford Pickover

* A First Course In Chaotic Dynamical Systems by Robert Devaney

Just some references from my "to read" collection.

https://en.wikipedia.org/wiki/Lorenz_system

I am lucky enough to have a 1st edition print, but there is now a free PDF online: https://sprott.physics.wisc.edu/SA.HTM