Flows with limited intersection of worldlines

TL;DR

This paper introduces a new class of flows with limited intersection of worldlines, constructs functional equations for them, and explores their connection to higher order differential equations using set embeddings.

Contribution

It defines flows with limited intersection of worldlines and develops functional equations for them, linking to higher order differential equations.

Findings

Constructed and solved functional equations for these flows.

Connected the concept to higher order ordinary differential equations.

Utilized set embeddings to analyze the flows.

Abstract

In this paper we define a flow with limited intersection of its worldlines and we construct and solve functional equations for such flow using a special kind of set embedding. For examples we use particular cases studied in the past by different authors. The connection to higher order ordinary differential equations is emphasized.