Ecosystem-wide move from Roots.jl to NonlinearSolve.jl

[Datseris]

I just saw the new NonlinearSolve.jl and the talk https://www.youtube.com/watch?v=O-2F8fBuRRg .

NonlinearSolve.jl seems to be better for us because it allows using the same syntax as the rest of SciML, while being more robust, with better developer support, faster, with better error handling, and with more algorithms. We should do an ecosystem-wide move to NonlinearSolve.jl.

Here are the points I recall from the top of my head that we use Roots.jl:

• PoincareMap at DynamicalSystemsBase.jl
• Takens estimator for fractal dimensions at FractalDimensions.jl
• Mean return times at ChaosTools.jl

Thanks to the developers of NonlinearSolve.jl which seem to be a large list (@ChrisRackauckas please pass on the thanks!)