I recently finished a course on dynamical systems supplemented by Strogatz's textbook. There are a few parts of the book that we didn't cover (in particular, the material on fractals), but the material that was covered was taught with a bit more detail than presented in Strogatz alone.

What's a good general dynamical systems textbook to "graduate" on to? Preferably, the book should not skimp out on theory and proofs.

I don't expect it to be self-contained in terms of topology material, but it would be nice if it were self-contained otherwise.

I don't mind books that skimp out on theory and proofs, if they otherwise present material in a unique way. Please write a little about why you recommand a particular textbook.

Some relevant M.SE questions:

Textbook Recommendation: Topological Dynamics


Two books you might consider are:

  1. Perko's Differential Equations and Dynamical Systems published by Springer.

  2. Guckenheimer, J and Holmes, P., Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields also published by Springer.

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  • 1
    $\begingroup$ Hi Richard. Many thanks for the recommendations (and welcome to M.SE!). Could you comment on a little on why you think these two books are appropriate? That's all that's left before I accept your answer :) $\endgroup$ – user89 Apr 21 '15 at 5:10
  • $\begingroup$ Hello Martin -- Both books present dynamical systems at a more advanced level than Strogatz. Given the level it should not be surprising that a book like Guckenheimer's requires a fairly advanced mathematical background, but it is the type of book that if you work through it carefully you should have what you need to begin doing research in this area. Neither book will skimp on theory. You might consider reading some of the reviews on Amazon. Also on Amazon you will also be able to browse a good portion of the book before you buy it. $\endgroup$ – Richard Apr 22 '15 at 4:40
  • $\begingroup$ @Richard: If you like, you can edit your answer to include the information in your comment above. $\endgroup$ – J W Apr 29 '15 at 20:54

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