Epsilon-equicontinuous points and epsilon-shadowable points (Q2116175)

The paper deals with discrete dynamical systems defined by a continuous self-map on a metric compact space without isolated points. The author introduces a new notion called \(\epsilon\)-equicontinuous point. In this setting he provides an example of a system \((X,f)\) such that that for very \(\epsilon\), there are \(\epsilon\)-equicontinuous points for \(f\) but \(f\) does not have any equicontinuous point. Properties of these type of points are studied and compared with inverse limit spaces. The notions of topological transitivity, \(\epsilon\)-shadowing and \(\epsilon\)-chain are discussed too.