arXiv subjects

Sergei Pilyugin

Publications and source records attributed to Sergei Pilyugin.

2 recordsLinked to original sources

arXiv2011

Dynamics near nonhyperbolic fixed points or nontransverse homoclinic points

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 periodic points are obtained. A new method, based on the study of the dynamics of center disks, is introduced. Some results on shadowing near a non-hyperbolic fixed point of a homeomorphism are obtained.

math.DS↗

arXiv2011

Lipschitz Shadowing for Flows

Let $ϕ$ be the flow generated by a smooth vector field $X$ on a smooth closed manifold. We show that the Lipschitz shadowing property of $ϕ$ is equivalent to the structural stability of $X$ and that the Lipschitz periodic shadowing property of $ϕ$ is equivalent to the $Ω$-stability of $X$.

math.DS↗