What would be the best book for me if I want to learn nonlinear dynamics ? I have my basics clear in linear differential equations, linear system theory, integral transforms and random process if they suffice as prerequisites.
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I think Strogatz's Nonlinear Dynamics and Chaos is a good introduction. A course's worth of his lectures teaching a class with this text is available online, as well. The lectures are on the YouTube channel "Cornell MAE" as a playlist.
Shlomo Sternberg's Dynamical Systems is a good companion or second book on this topic. It starts off at a slightly higher level of prerequisites, and has some overlap. I find this to be helpful, to get a more mathematical second look at some topics. As a bonus, Sternberg's text is a Dover publication, so it's inexpensive.
One of my profs also suggested me to start with Strogatz. In google books and in some lecture video i see the references are given from Hilborn ; how is that book ? Obviously i would go for the simplest one,whichever it is.
Strogatz is designed for an interdisciplinary course, so the prerequisites are rather low for this sort of book.
I haven't read Hilborn, but from the table of contents, it seems like he goes into more depth on fewer topics than Strogatz does. I can't say for sure, but it also looks like it has a higher level of difficulty, as material covered in the main body of Strogatz is in appendices in Hilborn. I'd say that Hilborn looks like a good book to check out of the library or borrow through interlibrary loan after having worked through most of Strogatz.