On approximation of relative entropies

MESON, ALEJANDRO M.; VERICAT, FERNANDO

JOURNAL OF DYNAMICAL SYSTEMS AND GEOMETRIC THEORIES

Taylor & Francis

Lugar: New Delhi; Año: 2023 vol. 21 p. 1 - 14

1726-037X

We analyze when symbolic dynamical systems have intermediaterelative entropies for two symbolic spaces (X, 1) and (Y, 2). By this is understoodto study the denseness of relative measure-theoretic entropies in theinterval [0, h(, 1)], where h(, 1) is a relative topological entropy of the shift1 with respect to a 2-invariant measure in Y . We prove that for irreducibleshifts with the (strong) specification property as introduced by Bowen,the set of the relative measure-theoretic entropies is dense in the above mentionedsense. To this, we use the decomposition of factor codes of Yoo and avariational principle for relative entropies given by Barral and Feng.