Oriented and standard shadowing properties for topological flows
Abstract
We prove that oriented and standard shadowing properties are equivalent for topological flows with finite singularites that are Lyapunov stable or Lyapunov unstable. Moreover, we prove that the direct product φ1 × φ2 of two topological flows has the oriented shdowing property if φ1 with finite singuralities has the oriented shadowing property, while φ2 has the limit set consisting of finite singularities that are Lyapunov stable or Lyapunov unstable.
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