Abstract
We study the metric mean dimension of Φ-irregular set in dynamical systems with the shadowing property. In particular, we prove that for dynamical systems with the shadowing property 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 are bounded from below by the respective values for class Y.
MATHEMATICS SUBJECT CLASSIFICATION:
Acknowledgments
We are grateful to the referees for their careful reading and their valuable comments and suggestions that helped to improve this paper and simplify some arguments.
Disclosure statement
No potential conflict of interest was reported by the author(s).