This article is cited in 1 paper

Large Systems

Geometric interpretation of entropy for Dyck systems

G. D. Dvorkin

Department of Mathematical Statistics and Random Processes, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

Abstract: We consider a relation between the metric entropy and the local boundary defor mation rate (LBDR) in the symbolic case. We show the equality between the LBDR understood as a limit almost everywhere and the entropy for a vast class of measures on Dyck systems.

Keywords: metric entropy, local boundary deformation rate, symbolic system, nonsynchronized system, invariant ergodic measure, regular bracket sequence, Dyck system.

UDC: 621.391 : 517.938 : 519.722

Received: 13.09.2021
Revised: 25.11.2021
Accepted: 26.11.2021

DOI: 10.31857/S0555292322020041

 English version: Problems of Information Transmission, 2022, 58:2, 137–143