Pregled bibliografske jedinice broj: 1106091
A surprising example for topological entropy of set-valued functions
A surprising example for topological entropy of set-valued functions // 2018 International Conference on Topology and its Applications - Book of abstracts
Náfpaktos, Grčka, 2018. str. 82-82 (predavanje, međunarodna recenzija, sažetak, znanstveni)
CROSBI ID: 1106091 Za ispravke kontaktirajte CROSBI podršku putem web obrasca
Naslov
A surprising example for topological entropy of
set-valued functions
Autori
Erceg, Goran ; Kennedy, Judy
Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni
Izvornik
2018 International Conference on Topology and its Applications - Book of abstracts
/ - , 2018, 82-82
Skup
International Conference on Topology and its Applications 2018
Mjesto i datum
Náfpaktos, Grčka, 07.07.2018. - 11.07.2018
Vrsta sudjelovanja
Predavanje
Vrsta recenzije
Međunarodna recenzija
Ključne riječi
Generalized inverse limit ; Topological entropy ; Invariant Cantor set ; Subshift of finite type ; Mahavier product
Sažetak
We generalize the definition of topological entropy due to Adler, Konheim, and McAndrew to set-valued functions (u.s.c. functions) from a closed subset of the interval to closed subsets of the interval. We use the Mahavier product of the graphs of u.s.c. functions viewed as closed subsets of [0, 1]^2. We show that this definition is indeed the generalization and that many of the properties of the topological entropy of continuous functions hold in this new setting. We compute topological entropy for various examples and finally give an example of a closed subset of the square with 0 entropy, but if any other point of the square is added, the new set has infinite entropy.
Izvorni jezik
Engleski
Znanstvena područja
Matematika
