Open AccessPacking dimensions of basins generated by distributions on a finite alphabet
Author(s) -
В. И. Бахтин,
Bruno Sadok
Publication year - 2021
Publication title -
žurnal belorusskogo gosudarstvennogo universiteta. matematika, informatika/žurnal belorusskogo gosudarstvennogo universiteta. matematika, informatika
Language(s) - English
Resource type - Journals
eISSN - 2617-3956
pISSN - 2520-6508
DOI - 10.33581/2520-6508-2021-2-6-16
Subject(s) - limit (mathematics) , alphabet , sequence (biology) , dimension (graph theory) , mathematics , space (punctuation) , finite set , structural basin , set (abstract data type) , packing dimension , combinatorics , geometry , mathematical analysis , computer science , geology , minkowski–bouligand dimension , paleontology , philosophy , linguistics , fractal dimension , biology , fractal , genetics , programming language , operating system
We consider a space of infinite signals composed of letters from a finite alphabet. Each signal generates a sequence of empirical measures on the alphabet and the limit set corresponding to this sequence. The space of signals is partitioned into narrow basins consisting of signals with identical limit sets for the sequence of empirical measures and for each narrow basin its packing dimension is computed. Furthermore, we compute packing dimensions for two other types of basins defined in terms of limit behaviour of the empirical measures.