TITLE: Reference book for "Dynamical Systems"
QUESTION [11 upvotes]: I want to do my thesis about oscillations. I am a math student so I enjoy rigorous texts and hate sketchy ones. I am looking for a textbook or a good source that could help me with dynamical systems. What I mean is an introductory book for it. 
For example I have enjoyed Real Mathematical Analysis by C.C. Pugh. I would greatly appreciate if someone could introduce me a book that could put everything about dynamical systems in perspective as good as it has been done in this book by Pugh (Pugh's is about analysis of course!).
Right now I started "Chaos: An Introduction to Dynamical Systems" by Alligood et al.
But I don't know if I am on the right track. So as a final sum-up:

To be rigorous 
To cover introductory stuff(or maybe even
advanced too!!)
Good text: this probably means the ability of
writer to intuitively pass the message beside being rigorous.

Thanks in advance.
P.S. I already see this but I find it irrelevant to my question.

REPLY [5 votes]: My favorites:

Differential Dynamical Systems - Meiss;
Differential Equations, Dynamical Systems and an Introduction to Chaos - Hirsch, Smale, Devaney;

Other good (and perhaps more rigorous) books:

Differential Equations and Dynamical Systems - Perko;
Introduction to Applied Nonlinear Dynamical Systems and Chaos -
Wiggins;

Reference containing plenty of solved examples and exercises:

Nonlinear Ordinary Differential Equations - An Introduction for
Scientists and Engineers - Jordan, Smith;

and the respective problem book

Nonlinear Ordinary Differential Equations - Problems and Solutions -
A Sourcebook for Scientists and Engineers - Jordan, Smith;

PS: I second Artem's opinion about Hale and Kocak's book; it's really nice.