Isoperiodic diagrams are used to investigate the topology of the codimension space of a representative dynamical system: the Hénon map. The codimension space is reported to be organized in a simple and regular way: instead of “structures-within-structures” it consists of a “structures-parallel-to-structures” sequence of shrimp-shaped isoperiodic islands immersed on a via caotica. The isoperiodic islands consist of a main body of principal periodicity k=1, 2, 3, 4, …, which bifurcates according to a period-doubling route. The Pk=k×2n, n=0, 1, 2, … shrimps are very densely concentrated along a main α-direction, a neighborhood parallel to the line b=−0.583a+1.025, where a and b are the dynamical parameters in Eq. (1). Isoperiodic diagrams allow to interpret and unify some apparently uncorrelated phenomena, such as ‘period-bubbling’, classes of reverse bifurcations and antimonotonicity and to recognize that they are in fact signatures of the complicated way in which period-doubling occurs in higher codimensional systems.
A transcendental Hénon map with an oscillating wandering Short $${\mathbb {C}}^2$$
