SOME RESULTS ON ENTROPY AND SEQUENCE ENTROPY

Autor:	Francisco Balibrea, V. Jiménez López, J. S. Cánovas Peña
Rok vydání:	1999
Předmět:	Pure mathematics Applied Mathematics Min entropy Topological entropy Topological entropy in physics Quantum relative entropy Combinatorics Rényi entropy Modeling and Simulation Maximum entropy probability distribution Engineering (miscellaneous) Entropy rate Joint quantum entropy Mathematics
Zdroj:	International Journal of Bifurcation and Chaos. :1731-1742
ISSN:	1793-6551 0218-1274
DOI:	10.1142/s0218127499001218
Popis:	In this paper we study some formulas involving metric and topological entropy and sequence entropy. We summarize some classical formulas satisfied by metric and topological entropy and ask the question whether the same or similar results hold for sequence entropy. In general the answer is negative; still some questions involving these formulas remain open. We make a special emphasis on the commutativity formula for topological entropy h(f ◦ g)=h(g ◦ f) recently proved by Kolyada and Snoha. We give a new elementary proof and use similar ideas to prove commutativity formulas for metric entropy and other topological invariants. Finally we prove a Misiurewicz–Szlenk type inequality for topological sequence entropy for piecewise monotone maps on the interval I=[0, 1]. For this purpose we introduce the notion of upper entropy.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::251297a0c38828894106a81dd43238f0 https://doi.org/10.1142/s0218127499001218 Zobrazit plný text záznamu