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JuliaDynamics / ChaosTools.jl

Tools for the exploration of chaos and nonlinear dynamics
https://juliadynamics.github.io/DynamicalSystemsDocs.jl/chaostools/stable/
MIT License
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Exploring chaotic motion through periodic orbits #163

Open Datseris opened 3 years ago

Datseris commented 3 years ago

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.58.2387

image

The authors also apply the algorithm to real-world data, and as such it has a nice place in a numerical package like DynamicalSystems.jl.

awage commented 3 years ago

One of the possible application of basins_of_attraction is finding UPO of maps with the Newton method (Yorke again):

https://doi.org/10.1016/S0167-2789(99)00138-4

Datseris commented 1 year ago

unstable periodic orbits can also be used to estimate a fractal dimension https://journals.aps.org/pra/abstract/10.1103/PhysRevA.37.1711 (same group of people again)