  In this work we introduce and explore a rescaled-theory of local stable and
unstable sets for rescaled-expansive flows and its applications to topological
entropy. We introduce a rescaled version of the local unstable sets and the
unstable points. We find conditions for points of the phase space to exhibit
non-trivial connected pieces of such unstable sets. We apply these results to
the problem of proving positive topological entropy for rescaled-expansive
flows with non-singular Lyapunov stable sets.
