Reference request: Nonlinear dynamics graduate reference

There are already a number of requests for textbooks detailing nonlinear stability theory, chaos theory etc. but many of them are more introductory (e.g. Strogatz - Nonlinear Dynamics and Chaos)

I've covered all this material before but I'm prone to forgetting the details. I hoped somebody might be able to point me in the direction of a more formal reference text on this subject. Perhaps a graduate level text, that covers major undergraduate material in a fairly mathematically rigorous way, as well as a little extra?

Here are two suggestions of the textbooks:

• Introduction to Applied Nonlinear Dynamical Systems and Chaos by Wiggins
• Differential Equations and Dynamical Systems by Perko

The second one is more or less self-contained, whereas the first one assumes good first ODE course (but reviews the necessary material). These are textbooks and not research monographs, which is more applicable to the texts in the other answer.

"Nonlinear Oscillations, Dynamical Systems ,and Bifurcation of Vector Fields" by John Guckenheimer and Philip Holmes comes to mind. I took a class on Dynamical Systems with the first author many years ago and this was the text. I see people using the book by Strogatz and always feel that it is just not at the same level.