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Normal Deterministic Diffusion in Two-Dimensional Tiled Dynamical Systems

A study of how a deterministic expanding map on a plane tiled by regular triangles or hexagons produces normal (Gaussian) diffusion of probability densities. Learners see how a matrix-valued Perron-Frobenius operator acting on the tile-type densities is diagonalized through the Fourier transform, yielding an asymptotically Gaussian density and an explicit diffusion coefficient set by the expansion factor.

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Deterministic diffusion in dynamical systems with a tiled phase space

Deterministic diffusion is the phenomenon in which a fully deterministic but chaotic dynamical system spreads an initial probability density into an asymptotically Gaussian distribution, so that its …