On the Maximal Sets for F-Expansive Measures

Villavicencio H. · Proyecciones (2026) · DOI: 10.22199/issn.0717-6279-4522

Resumen

In this paper we fix a continuous flow ϕ on a compact metric space and a Borel probability measure µ which is F-expansive for some family F of reparametrizations. We study how far F can be enlarged while preserving expansivity of µ. Whenever a maximal family exists (relative to F and with respect to inclusion), we prove that it is clopen in the reparametrization space (H, db), hence a union of its connected components. As a consequence, every F-expansive measure is Bf-expansive for all f ∈ F. We also present an explicit example showing that maximal families may be proper subsets of H.

Instituciones: Universidad Nacional de Ingeniería