In the early 70s, Igor Gumowski and Christian Mira studied families of maps obtained from a dissipative perturbation of conservative maps issued from the studies on the problem of ``stochastic’’ instability in accelerators and storage rings . Among these two families, there is a two-dimensional quasi-conservative map which may be written as
where parameters values were and , being the bifurcation parameter. This two-dimensional map was published in 1973  and republished in 1980 . Two chaotic attractors were presented as being ``stochastic’’ in 1973 (Fig. 1).
 C. Mira, Memories of the early days of chaos theory in The Chaos avant-garde, World Scientific Series on Nonlinear Science A, 39, pp. 95-197, 2000.
 J. Bernussen, Liu Hsu & C. Mira, Quelques exemples du second ordre, Collected preprints of Colloque International du CNRS, 229, Transformations ponctuelles et applications (Toulouse, September 1973), Proceedings Editions du CNRS (Paris), pp. 195-226, 1976.
 I. Gumowski & C. Mira, Recurrences and discrete dynamic systems : An introduction, Lecture Notes in Mathematics, 809, 1980.