Baker's Map

In dynamical systems theory, the baker's map is a chaotic map from the unit square into itself, named after the kneading operation bakers apply to dough: the dough is cut in half, the two halves are stacked on each other, and the result is compressed. The map can be understood as the bilateral shift operator of a bi-infinite two state lattice model, and it is topologically conjugate to the horseshoe map; in physics, a chain of coupled baker's maps can be used to model deterministic diffusion. Like many deterministic dynamical systems it is studied through its action on the space of functions defined on the unit square, an operator known as the transfer operator of the map, and the baker's map is an exactly solvable model of deterministic chaos in that the eigenfunctions and eigenvalues of its transfer operator can be found explicitly.