Oriented and standard shadowing properties for topological flows. (English) Zbl 1536.37027
Summary: We prove that oriented and standard shadowing properties are equivalent for topological flows with finite singularities that are Lyapunov stable or backward Lyapunov stable. Moreover, we prove that the direct product \(\phi_1 \times \phi_2\) of two topological flows has the oriented shadowing property if \(\phi_1\) with finite singularities has the oriented shadowing property, while \(\phi_2\) has the limit set consisting of finite singularities that are Lyapunov stable or backward Lyapunov stable.
MSC:
| 37B65 | Approximate trajectories, pseudotrajectories, shadowing and related notions for topological dynamical systems |
| 37B25 | Stability of topological dynamical systems |
References:
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