Resumen de Topological Complexity: Entropy Point, Metric Mean Dimension in Control Systems

Rui Yang, Ercai Chen, Xiaoyao Zhou

• We introduce two new notions to describe the topological complexity of control systems. We first introduce a notion called entropy point to characterize zero and positive outer invariance entropy systems, then we introduce a notion called metric mean dimension to characterize the growth of infinite outer invariance entropy systems and establish a variational principle for it in terms of local entropy function that is related to outer invariance entropy. Finally, we establish a product invariance entropy formula under some conditions.