A cohomological Conley index for maps on metric spaces

AbstractWe define a cohomological Conley index of an isolated invariant set of a time-discrete semidynamical system on a metric space. We prove the homotopy invariance and the additivity properties of the index. For applications to time-periodic parabolic partial differential equations (PDEs) the reader is referred to the authors' paper: Nontrivial full bounded solutions of time-periodic semilinear parabolic PDEs (Proc. Roy. Soc. Edinburgh, to appear)