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In this short exposition, we describe equilibria and periodic orbits in termsof the flow map, {\Phi}, and discuss the essentials of the Jacobian-freeNewton-Krylov (JFNK) method that can be used to find them. This method requireslittle more than calls to an existing time stepping code, which {\Phi} can beconsidered to represent. Fortran90 / MATLAB code is available to try it out foryourself, where, in the template/example the method is applied to the Lorenzsystem. This code is problem-independent and can be applied to large systems,having initially been developed to find periodic orbits in simulations of pipeflow.

Equilibria, periodic orbits and computing them