Global Bifurcations and Explosions
Nonsmooth systems suffer a curse of dimensionality. Every higher dimension brings the possibility of fundamentally new local and global dynamics, as a simple object classified in low dimensions takes on unknown new complications in higher dimensions. Classifying these conventionally, by forming an accounting of all singularities and their unfoldings, can therefore make little impact on our studies in higher dimensions. As with the exit points which we used to organize local dynamics in Chapter 10, we need another approach.
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