### 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, < i> The Conley index

over a base< /i> , Trans. Amer. Math. Soc. < b> 352< /b> (2000), 4171-4194].

We also compare it to other Conley-type

indices and prove its continuation property.

definition is an alternative for the Conley index over a base

defined in [M. Mrozek, J.F. Reineck and R. Srzednicki, < i> The Conley index

over a base< /i> , Trans. Amer. Math. Soc. < b> 352< /b> (2000), 4171-4194].

We also compare it to other Conley-type

indices and prove its continuation property.

#### Keywords

Conley index; isolated invariant set; continuation

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