Metric entropy of capacity preserving dynamical systems

Metric entropy is an important isomorphic invariant in classical ergodic theory and it is one of the most accepted tools to characterize the complexity of dynamical systems. A capacity is a real-valued function but it is not additive. In contrast to the traditional measure preserving systems, the more general capacity preserving systems are investigated and an analogical metric entropy is introduced for such systems. The properties of metric entropy with respect to capacities are explored and comparison with the classical metric entropy is conducted. (c) 2022 Elsevier B.V. All rights reserved.