A differential algorithm for the Lyapunov spectrum
It offers a new method for computing Lyapunov exponents in dynamical systems, but is demonstrated only on a simple example without quantitative comparison to existing methods.
The paper introduces a continuous algorithm for computing the full Lyapunov spectrum that avoids rescaling by using a matrix differential equation, demonstrated on a particle between contracting walls.
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.