Andrey Shilnikov studies bifurcation theory and dynamical systems. With Leonid Pavlovich Shilnikov, he authored an account of the Shilnikov bifurcation, explaining how a homoclinic orbit to a saddle-focus can produce complicated dynamics. The construction connects local contraction and expansion near an equilibrium with a global return of its unstable manifold.[ref]
Shilnikov Bifurcation by Leonid Pavlovich Shilnikov and Andrey Shilnikov. Saddle-focus and Shilnikov theorem sections
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