Embedding theorems for discrete dynamical systems and topological flows

TL;DR

This paper explores embedding theorems for topological flows and discrete systems, providing new proofs and extending existing results to suspension flows, thereby advancing the understanding of topological dynamics.

Contribution

It introduces a new embedding theorem for discrete topological systems and extends results to suspension flows, including a novel proof of the Gutman-Jin embedding theorem.

Findings

Established an embedding theorem for discrete topological systems.

Extended embedding results to suspension flows via constant functions.

Provided a new proof of the Gutman-Jin embedding theorem.

Abstract

In this paper, we investigate the embeddings for topological flows. We prove an embedding theorem for discrete topological system. Our results apply to suspension flows via constant function, and for this case we show an embedding theorem for suspension flows and give a new proof of Gutman-Jin embedding theorem.