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.



Dynamical Systems for undergraduate students
I would recommend reading through [*Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering*](http://www.google.com/products/catalog?q=nonlinear+dynamics+and+chaos&oe=utf-8&rls=org.mozilla%3Aen-US%3Aofficial&client=firefox-a&um=1&ie=UTF-8&tbm=shop&cid=3730006166953307001&sa=X&ei=rW57Tpy7DMnt0gH04uzAAg&ved=0CEAQ8wIwAQ) by Steven Strogatz. He does a great job of motivating the applications of the field to various branches of science with a plethora of exercises. I wouldn't say it's entirely rigorous at times, but it covers a huge amount of material which should give you plenty to think about if you want to do a research topic. Out of all the books I've seen on the subject, his is probably the only elementary one that tackles renormalization techniques and universality, involving [Feigenbaum's constant](http://en.wikipedia.org/wiki/Feigenbaum_constants). 


