Anyone have any suggestions for the following situation/question? (help wanted, please!)
I understand the theory (c.f., Perko or Nayfeh and Balachandran, Ch.3), but I do not understand how this is accomplished numerically:
Given a (chaotic) dynamical system (for example, I am using the Lorenz system with standard parameters), if I have numerically found (stabilized) an unstable periodic orbit, how would I find the UPO's Floquet multiplier? Note that since the system is nonlinear, there is no explicit formula for the UPOs. In the big picture, what I am trying to do is investigate the various calculations on a chaotic system (dimension, natural measure, etc) that can be approximated by having obtained this information from UPOs (e.g., its numerical stability or Lyapunov exponent).
I am aware that similar questions have been asked here on Stack Exchange:
How to calculate floquet exponents
but in neither thread is this process demonstrated numerically. The examples in my textbooks all assume an explicit formula for the periodic orbit. Once again, I understand the theory, but not its practice, especially in my case when I do not have an explicit formula for the UPO, just a $(N\times 3)$ matrix of orbit time steps ($N$ is the number of time steps from my UPO solver). I am familiar with Matlab, C/C++, and Python.
Thank you!