CRM: Centro De Giorgi
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School on Hyperbolic Dynamics

poster: Shadowable Points for Flows

speaker: Jesús Aponte (Ph.D. Student in Mathematics UFRJ, Rio de Janeiro, Brasil)

abstract: We introduce the notions of shadowable points for flows by extending the notion of shadowable points for homeomorphism. We prove that the set of shadowable points for flows satisfy the following properties: the set of shadowable points is invariant and a \(G{\delta})\- set. A flow has the pseudo-orbit tracing property if and only if every point is shadowable. The chain recurrent and nonwandering sets coincide when every chain recurrent point is shadowable. The shadowable points coincide with the finitely shadowable points when the flow is nonsingular. We characterize the set of forward shadowable points for transitive flows and chain transitive flows. We prove that the geometric Lorenz attractor does not have shadowable points.

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