Two-dimensional solvable chaos

Two methods are proposed to construct two-dimensional chaotic maps. Several examples of exactly solvable chaotic maps and their invariant measures are obtained. They are isomorphic maps of square to square, plane to plane and circle to circle having various symmetry such as uniform, rotational and the quartic rotational symmetry.

► Inverse problem finding chaotic maps with given invariant measure is proposed and discussed.
► Several new examples of two-dimensional solvable chaos are given.
► These maps can be used as random number generators.