46 citations · 254 across the 37 of their papers we have counts for
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math.DS2013★ 24 cited
Showcase of Blue Sky Catastrophes
Leonid Shilnikov, Andrey Shilnikov, Dmitry Turaev
Let a system of differential equations possess a saddle-node periodic orbit such that every orbit in its unstable manifold is homoclinic, i.e. the unstable manifold is a subset of…
math.DS2013★ 15 cited
Oscillating mushrooms: adiabatic theory for a non-ergodic system
V. Gelfreich, V. Rom-Kedar, D. Turaev
Can elliptic islands contribute to sustained energy growth as parameters of a Hamiltonian system slowly vary with time? In this paper we show that a mushroom billiard with a period…