Leonid Pavlovich Shilnikov developed the theory of Shilnikov bifurcations associated with a saddle-focus. The Shilnikov bifurcation explains a route to chaos through the return of an unstable manifold to the same equilibrium. His joint account with Andrey Shilnikov describes the role of the saddle quantity in distinguishing stable periodic behavior from more complicated nearby dynamics.[ref]
Shilnikov Bifurcation by Leonid Pavlovich Shilnikov and Andrey Shilnikov. Shilnikov theorem section
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