# N-expansive Flows

## TL;DR

This paper introduces the concept of N-expansivity for flows, extending existing results, providing examples, and establishing relationships with other forms of expansivity, especially on compact surfaces.

## Contribution

It defines N-expansivity for flows, compares it with CW-expansiveness, and proves implications on compact surfaces, advancing the theoretical understanding of flow dynamics.

## Key findings

- Examples of N-expansive but not expansive flows
- Examples of CW-expansive but not N-expansive flows
- On compact surfaces, N-expansivity implies Komuro expansivity

## Abstract

We define the concept of $N$-expansivity for flows and extend some of the results already established for discrete dynamics and for $CW$-expansive flows. We show examples of $N$-expansive flows but not expansive, and examples of $CW$-expansive flows but not $N$-expansive for any natural number $N$.} We also define Komuro $N$-expansivity and prove that on compact surfaces it implies Komuro expansivity.