  In this short exposition, we describe equilibria and periodic orbits in terms
of the flow map, {\Phi}, and discuss the essentials of the Jacobian-free
Newton-Krylov (JFNK) method that can be used to find them. This method requires
little more than calls to an existing time stepping code, which {\Phi} can be
considered to represent. Fortran90 / MATLAB code is available to try it out for
yourself, where, in the template/example the method is applied to the Lorenz
system. This code is problem-independent and can be applied to large systems,
having initially been developed to find periodic orbits in simulations of pipe
flow.
