I’m currently reading Brin and Stuck’s Introduction to Dynamical Systems, and I think I like the field a lot so far. I haven’t finished it quite yet, but what are some other good textbooks I can read after Brin and Stuck’s very good general introduction? I like pretty much all the fields presented so far, especially topological dynamics and differentiable dynamics.
There is an encyclopedic book of A. Katok and B. Hasselblatt, Introduction to the modern theory of dynamical systems. Encyclopedia of Mathematics and its Applications, 54. Cambridge University Press, Cambridge, 1995 which covers most of the subject, and requires minimal background.
Among the more specialized, smaller books, I like Z. Nitecki, Differentiable dynamics.
But dynamics is a vast subject, with many branches, and there are very many good books. On the very popular subject of Holomorphic dynamics, the best introductory book on my opinion is J. Milnor, Dynamics in one complex variable (available of the arxiv).
There is also the classic Palis, de Melo: Geometric Theory of Dynamical Systems.
If you want to follow up on chapter 3 of Brin & Stuck, I recommend An Introduction to Symbolic Dynamics by Doug Lind and Brian Marcus (Cambridge, 1995).