Baker's map

The baker's map can be understood as the bilateral shift operator of a bi-infinite two-state lattice model.

In physics, a chain of coupled baker's maps can be used to model deterministic diffusion.

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 is an exactly solvable model of deterministic chaos, in that the eigenfunctions and eigenvalues of the transfer operator can be explicitly determined.

One definition folds over or rotates one of the sliced halves before joining it (similar to the horseshoe map) and the other does not.

The spectrum is continuous, and because the operator is unitary the eigenvalues lie on the unit circle.

The baker's map can be understood as the two-sided shift operator on the symbolic dynamics of a one-dimensional lattice.

as and In this representation, the shift operator has the form which is seen to be the unfolded baker's map given above.