48 citations · 97 across the 10 of their papers we have counts for
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math.DS2011
Dynamics near nonhyperbolic fixed points or nontransverse homoclinic points
Sergey Kryzhevich, Sergei Pilyugin
We study dynamics in a neighborhood of a nonhyperbolic fixed point or an irreducible homoclinic tangent point. General type conditions for the existence of infinite sets of periodi…
math.DS2011★ 2 cited
Lipschitz Shadowing for Flows
Kennet J. Palmer, Sergei Pilyugin, Sergey Tikhomirov
Let be the flow generated by a smooth vector field on a smooth closed manifold. We show that the Lipschitz shadowing property of is equivalent to the structural stabili…