Abstract

We prove that oriented and standard shadowing properties are equivalent for topological flows on closed surfaces with the nonwandering sets consisting of a finite number of critical elements (i.e., singularities or closed orbits). Moreover, we prove that each isolated singularity of a topological flow on a closed surface with the oriented shadowing property is either asymptotically stable, backward asymptotically stable, or admits a neighborhood which splits into two or four hyperbolic sectors.

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