I'm looking for a textbook discussing logistic map and chaos theory that is:
- Mathematically rigorous. In definition-theorem format (because I like it when the steps are clear, concrete and compact). But preferably more focused on the algebraic results, than on defining objects merely for an alternate mathematical perspective.
- Contains algebraic results in line with recent research. I'm aware much of chaos cannot be explained algebraically yet.
- Can contain numerical explanations too, but not overstepping the algebraic ones.
I read some chapters from Strogatz. It's nice but doesn't say much about algebraic results of logistic map beyond the 2-period cycle and it's not 100% clear because he omits some steps and definitions.
Edit: Suggestions are appreciated even if they don't satisfy all the points. But no pop-sci please.