When I took a course on dynamical systems my lecturer recommended A First Course in Dynamics by Boris Hasselblatt and Anatole Katok and Introduction to Dynamical Systems by Michael Brin and Garrett Stuck. These are of course both technical books for the nitty gritty mathematics behind it all, for a more readable overview I would go for either the Strogatz book or try The Essence of Chaos by Edward Lorenz.