An explicit compact universal space for real flows

Abstract

The Kakutani-Bebutov Theorem (1968) states that any compact metric real flow whose fixed point set is homeomorphic to a subset of $\mathbb{R}$ embeds into the Bebutov flow, the $\mathbb{R}$-shift on $C(\mathbb{R},[0,1])$. An interesting fact is that this universal space is a function space. However, it is not compact, nor locally compact. We construct an explicit countable product of compact subspaces of the Bebutov flow which is a universal space for all compact metric real flows, with no restriction; namely, into which any compact metric real flow embeds. The result is compared to previously known universal spaces.

17 pages

References in corpus (2)

• Mean Dimension & Jaworski-type Theorems
• Embedding minimal dynamical systems into Hilbert cubes

Cited by in corpus (2)

• A Lipschitz refinement of the Bebutov--Kakutani dynamical embedding theorem
• A new universal real flow of the Hilbert-cubical type