On some dynamical properties of S-unimodal maps on an interval
We study dichotomous behavior of solutions to a non-autonomous linear difference equation in a Hilbert space. The evolution operator of this equation is not continuously invertible and the corresponding unstable subspace is of infinite dimension in general. We formulate a condition ensuring the dichotomy in terms of a sequence of indefinite metrics in the Hilbert space. We also construct an example of a difference equation in which dichotomous behavior of solutions is not compatible with the signature...
If a continuous map f of a compact metric space has the pseudo orbit tracing property and is h-expansive then the set of all fixed points of f is totally disconnected.