Symbolic Codes for Rotational Orbits

Symbolic codes for rotational orbits and "islands-around-islands" are constructed for the quadratic, area-preserving Henon map. The codes are based upon continuation from an anti-integrable limit or, alternatively, from the horseshoe. Given any sequence of rotation numbers we obtain symbolic sequences for the corresponding elliptic and hyperbolic rotational orbits. These are shown to be consistent with numerical evidence. The resulting symbolic partition of the phase space consists of wedges constructed from images of the symmetry lines of the map.