2015/12/03 by Udayan B. Darji, Darji, Udayan B., Étienne Matheron +1
Mathematics · #47A99 #54H20 #Dynamical Systems (math.DS) #FOS: Mathematics #Primary: 37B99 #Secondary: 54C20 #math.DS #msc:37B99 #msc:47A99 #msc:54C20 #msc:54H20
paper · pdf · doi:10.48550/arxiv.1512.01266
15 pages
arxiv created 2015/12/03 · arxiv updated 2015/12/07
We prove some "universality" results for topological dynamical systems. In particular, we show that for any continuous self-map T of a perfect Polish space, one can find a dense, T-invariant set homeomorphic to the Baire space \mathbb N\mathbb N; that there exists a bounded linear operator U: ℓ1 → ℓ1 such that any linear operator T from a separable Banach space into itself with \Vert T\Vert≤ 1 is a linear factor of U; and that given any σ-compact family \mathcal F of continuous self-maps of a compact metric space, there is a continuous self-map U\mathcal F of \mathbb N\mathbb N such that each T∈ \mathcal F is a factor of U\mathcal F.