This package provides a Julia implementation of the Numerical Analysis of Fundamental Frequencies (NAFF) method by J. Laskar to compute fundamental frequencies of quasi-periodic systems to high precision. The evolution of the fundamental frequencies with time can be used to measure chaos. Some papers of interest:
- The chaotic motion of the solar system: A numerical estimate of the size of the chaotic zones
- Application of Frequency Map Analysis to the ALS
FundamentalFrequencies.jl in particular is implemented in a branchless and vectorized way for GPU-accelerated, batched NAFF. With this package, one can do NAFF on e.g. a million particles in parallel on a GPU. While this was initially developed for the SciBmad accelerator physics code, the tools developed here may be useful to a much broader nonlinear dynamics audience.