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I'm interested in understanding the dynamics of the discrete Landau-Lifshitz system. It's solutions to equations like $$\frac{\partial X_n}{\partial t} = X_n\times (X_{n-1}+X_{n+1})$$ where the $X_n$ are unit vectors in spheres that sit on a discrete lattice (parameterized by $n$, and possibly finite with boundary conditions or infinite). This system is Hamiltonian, but apparently it is also very chaotic/non-integrable.

I'm not interested in understanding the associated quantum or continuum system (although I'm aware they are related).

Does anyone know a good paper that discusses the dynamics of these classical systems? In particular, one that explains their non-integrability and chaotic behaviour?

I'm sorry if this question isn't appropriate here.

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This is currently the reference I'm working with since it seems to be the most mathematical/recent/comprehensive, but it doesn't prove or explain any details. arxiv.org/abs/1101.1005v1 – Jeremy Lane Feb 27 '14 at 22:56

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