A new universal real flow of the Hilbert-cubical type

Abstract

We provide a new universal real flow of the Hilbert-cubical type. We prove that any real flow can be equivariantly embedded in the translation on $L(\mathbb{R}{)}^{\mathbb{N}}$, where $L(\mathbb{R})$ denotes the space of $1$-Lipschitz functions $f:\mathbb{R}\to [0,1]$. Furthermore, all those functions in $L(\mathbb{R}{)}^{\mathbb{N}}$ that are images of such embeddings can be chosen as $C^1$-functions.