A differential algorithm for the Lyapunov spectrum

We present a new algorithm for computing the Lyapunov exponents spectrum based on a matrix differential equation. The approach belongs to the so-called continuous type, where the rate of expansion of perturbations is obtained for all times, and the exponents are reached as the limit at infinity. It does not involve exponentially divergent quantities so there is no need of rescaling or realigning of the solution. We show the algorithm’s advantages and drawbacks using mainly the example of a particle moving between two contracting walls.

► A new algorithm for computing the Lyapunov exponents spectrum is presented.
► This algorithm is based on a matrix differential equation.
► This method is dedicated for the general relativity and cosmology systems.
► The main advantage of the base method is its covariant nature and concise.
► This framework can be used to obtain some analytic results.