  It is a paper about models for isolated sets and the construction of special
hyperbolic Lyapunov functions. We prove that after a suitable surgery every
isolated set is the intersection of an attractor and a repeller. We give linear
models for attractors and repellers. With these tools we construct hyperbolic
Lyapunov functions and metrics around an isolated set whose values along the
orbits are catenary curves. Applications are given to expansive flows and
homeomorphisms, obtaining, among other things, a hyperbolic metric on local
cross sections for an arbitrary expansive flow on a compact metric space.
