I'm taking a course on it right now and most people I've seen use Steven Strogatz's book (Nonlinear Dynamics and Chaos). He mostly focuses on continuous system

I'm taking a course on it right now and most people I've seen use Steven Strogatz's book (Nonlinear Dynamics and Chaos). He mostly focuses on continuous systems, but the end of the book has a lot on discrete stuff like logistic maps and fractals. His book is definitely the book on stuff like this, but mostly oriented at math-modelling and differential equations. Its also very easy to read and get through with lots of really great examples. I obviously haven't yet looked at the research you are trying to dig into, but definitely check out this book from the library at least. Its also not that expensive.