@article{Lee2022, 
author = {Manseob Lee},
title = {Flows with ergodic pseudo orbit tracing property},
year = {2022},
journal = {Electronic Research Archive},
volume = {30},
number = {7},
pages = {2406-2416},
keywords = {hyperbolic, pseudo orbit tracing property, ergodic pseudo orbit tracing property, chain transitive, transitive, star condition},
url = {https://www.sciopen.com/article/10.3934/era.2022122},
doi = {10.3934/era.2022122},
abstract = {In the manuscript, we deal with a type of pseudo orbit tracing property and hyperbolicity about a vector field (or a divergence free vector field). We prove that a vector field (or a divergence free vector field) of a smooth closed manifold  M has the robustly ergodic pseudo orbit tracing property then it does not contain any singularities and it is Anosov. Additionally, there is a dense and open set  R in the set of  C1 a vector field (or a divergence free vector field) of a smooth closed manifold  M such that given a vector field (or a divergence free vector field) has the ergodic pseudo orbit tracing property then it does not contain singularities and it is Anosov.}
}