Recommend resources on dynamical systems and singularities

Question

I'm looking for resources on bifurcation theory and systems of non-linear differential equations, but am very particular about the way it is taught/explained. I would like the approach to be based on bifurcation diagrams, and analysing singularities, in particular cusp, isola and double limit point singularities.

Unfortunately I cannot find much could material on this topic.

I would prefer free online resources/lecture notes etc, but also book recommendations would be great.

Thanks

Answer 1

Have you looked through anything by V. I. Arnold? The book " Geometrical Methods in the Theory of Differential Equations" might be of interest to you.

Also, John Guckenheimer would be another reference for studying problems in bifurcation theory. Home Page: http://www.math.cornell.edu/~gucken/