2011/06/01 by Bobok, Jozef, Bruin, Henk
#Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1106.0111
We investigate some properties of (universal) Banach spaces of real functions in the context of topological entropy. Among other things, we show that any subspace of C([0,1]) which is isometrically isomorphic to ℓ1 contains a functions with infinite topological entropy. Also, for any t ∈ [0, ∞], we construct a (one-dimensional) Banach space in which any nonzero function has topological entropy equal to t.