Logarithmic Expansion, Entropy, and Dimension for Set-Valued Maps

Carrasco-Olivera D.; Metzger R.; Morales C.A. · Journal of Mathematical Sciences (United States) (2023) · DOI: 10.1007/s10958-023-06737-y

Resumen

We obtain a lower bound for the entropy of a Borel probability measure (not necessarily invariant) with respect to an upper semicontinuous set-valued map as the product of the lower dimension of the measure and the logarithmic expansion rate. This is a generalization of the well-known measure-preserving single-valued case.

Instituciones: Universidad Nacional de Ingeniería