The parameter space of the Hénon map is reported to contain a regular structure-parallel-to-structure sequence of shrimp-shaped robust isoperiodic domains. They appear densely concentrated on a neighborhood along a main α direction, extending across both orientation-preserving and -reversing domains. There is also a secondary β direction, roughly perpendicular to a very dense ‘‘foliation of legs’’ emanating from the isoperiodic domains. Familiar bifurcation phenomena observed in unimodal maps correspond to particular cuts along the β direction. The α direction is rich in new phenomena. The topology along α is conjectured to be typical of bimodal maps.

• Received 21 September 1992

DOI:https://doi.org/10.1103/PhysRevLett.70.2714