Abstract
For a mapping of the torusT 2 we propose a definition of the diffusion coefficientD suggested by the solution of the diffusion equation ofT 2. The definition ofD, based on the limit of moments of the invariant measure, depends on the set Ω where an initial uniform distribution is assigned. For the algebraic automorphism of the torus the limit is proved to exist and to have the same value for almost all initial sets Ω in the subfamily of parallelograms. Numerical results show that it has the same value for arbitrary polygons Ω and for arbitrary moments.
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Siboni, S., Turchetti, G. & Vaienti, S. Diffusion on the torus for Hamiltonian maps. J Stat Phys 75, 167–187 (1994). https://doi.org/10.1007/BF02186285
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DOI: https://doi.org/10.1007/BF02186285