Topological entropy on closed sets in [0,1]2 (CROSBI ID 255361)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Erceg, Goran ; Kennedy, Judy
engleski
Topological entropy on closed sets in [0,1]2
We generalize the definition of topological entropy due to Adler, Konheim, and McAndrew [1] to set-valued functions from a closed subset A of the interval to closed subsets of the interval. We view these set-valued functions, via their graphs, as closed subsets of [0, 1]^2. We show that many of the topological entropy properties of continuous functions of a compact topological space to itself hold in our new setting, but not all. We also compute the topological entropy of some examples, relate the entropy to other dynamical and topological properties of the examples, and we give an example of a closed subset G of [0, 1]^2 that has 0 entropy but G U {; ; ; ; (p, q)}; ; ; ; , where (p, q) is an element of [0, 1]^2 \ G, has infinite entropy.
Generalized inverse limit ; Topological entropy ; Invariant Cantor set ; Subshift of finite type ; Mahavier product
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Podaci o izdanju
246
2018.
106-136
objavljeno
0166-8641
1879-3207
10.1016/j.topol.2018.06.015