The Conley index over a phase space for flows

Abstract

We construct the Conley index over a phase space for flows. Our definition is an alternative for the Conley index over a base defined in [M. Mrozek, J.F. Reineck and R. Srzednicki, The Conley index over a base, Trans. Amer. Math. Soc. 352 (2000), 4171-4194]. We also compare it to other Conley-type indices and prove its continuation property.