Metric mean dimension of irregular sets for maps with shadowing

Abstract

We study the metric mean dimension of Φ-irregular set IΦ(f ) in dynamical systems with the shadowing property. In particular we prove that for dynamical systems with shadowing containing a chain recurrent class Y , the values of topological entropy together with the values of lower and upper metric mean dimension of the set IΦ(f )∩ B(Y, ε) ∩ CR(f ) are bounded from below by the respective values for class Y .