I recently finished a course on dynamical systems supplemented by Strogatz's textbook. There are a few parts of the book that we didn't cover (in particular, the material on fractals), but the material that was covered was taught with a bit more detail than presented in Strogatz alone.
What's a good general dynamical systems textbook to "graduate" on to? Preferably, the book should not skimp out on theory and proofs.
I don't expect it to be self-contained in terms of topology material, but it would be nice if it were self-contained otherwise.
I don't mind books that skimp out on theory and proofs, if they otherwise present material in a unique way. Please write a little about why you recommand a particular textbook.
Some relevant M.SE questions: