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Baker's map

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High Quality Content by WIKIPEDIA articles! In dynamical systems theory, the baker's map is a chaotic map from the unit square into itself. It is named after a kneading operation that bakers apply to dougt, the dough is cut in half, and the two halves are stacked on one-another, and compressed. The word baker is not a name, so it should not be capitalized. The baker's map can be understood as the bilateral shift operator of a bi-infinite two-state lattice model. The baker's map is topologically conjugate to the horseshoe map. In physics, a chain of coupled baker's maps can be used to model deterministic diffusion. The Poincaré recurrence time of the baker's map is short compared to Hamiltonian maps. As with many deterministic dynamical systems, the baker's map is studied by its action on the space of functions defined on the unit square. The baker's map defines an operator on the space of functions, known as the transfer operator of the map. The baker's map is an exactly solvable model of deterministic chaos, in that the eigenfunctions and eigenvalues of the transfer operator can be explicitly determined.