A new universal real flow of the Hilbert-cubical type

TL;DR

This paper introduces a new universal real flow of the Hilbert-cubical type, demonstrating that any real flow can be embedded into a space of Lipschitz functions, with embeddings that can be chosen as smooth functions.

Contribution

It constructs a novel universal real flow of the Hilbert-cubical type and shows all embeddings can be realized with smooth functions.

Findings

Any real flow can be embedded into the translation on $L( eal)^\nat$.

Embeddings can be chosen as $C^1$-functions.

Provides a new universal model for real flows.

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.