N-expansive Flows

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.