Units: Remarkable points in dynamical systems

In number theory, “units” are very special numbers characterized by having their norm equal to unity. So, in the real quadratic field (√3) the number of −2 + √3 −0.2679491924… is a unit because (−2 + √3) (−2 - √3) = 1. In this paper we determine precisely the numerical values of the coordinates of some points defined by multiple intersections of domains of stability in the parameter space of the Hénon map and, in all cases considered for which analytical calculations were feasible, find that such intersection points are invariably defined by units and by simple functions of units. The very special points defined by units are analogous to the familiar multicritical points in phase diagrams. Some simple consequences of the precise dynamics on the ground fields enforced by the equations of motion are discussed