Abstract
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.
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