TITLE: Dynamical Systems for undergraduate students
QUESTION [6 upvotes]: Hello,
I'm searching for a good subject of Dynamical Systems theory in which I can propose a theme for a undergraduate research opportunity program. As I'm a undergraduate student, I have had only be exposed to subjects such as linear and abstract algebra, real analysis (calculus, basic topology of $\mathbb{R}^{n}$, metric spaces, and a "informal" view of measure theory). 
I have been looking at subjects such as unidimensional dynamics and circle homeomorphisms, and reading An Introduction to Chaotic Dynamical Systems by R. Devaney.
-Thanks.

REPLY [3 votes]: I see that you have already received suggestions about books, so I am not going to suggest any books, but I will suggest a topic, if that's what you are looking for. I think the notion of entropy and its role in dynamical systems could potentially be a good research theme. You can find out about different notions of entropy, their connections and their importance in dynamical systems.