Before the emergence of chaos in electronic circuits during the late 70s and early 80s there is an important contribution by Igor Gumowski & Christian Mira (the “Toulouse Research Group”) whose a short story was given in Ref. . Stimulated by a paper by C. P. Pulkin  who showed that in one-dimensional noninvertible map infinitely many unstable cycles may lead to bounded complex iterated sequences, Gumowski & Mira studied the piecewise-linear map  
For some -values, they obtained an attractive limit set made of bounded cloud of points as shown in Fig. 1 (). This could be the very the first “chaotic” solution to a piecewise-linear map reported with an explicit picture. In the original paper (1968), Mira mentioned that
La récurrence inverse de [l’application ci-dessus] permet, en prenant une condition initiale voisine de 0 (point double stable), de constater qu’il existe un cycle d’ordre très élevé, peut-être infini.
By these times, Gumowski & Mira indicated these types of behaviors as “Pulkin phenonmenon”. This is only ten years later that first chaotic solutions were widely investigated in electronic circuits.
Increasing slightly the value to 2.39, the chaotic solution observed is just before a boundary crisis unifying the two sets of points (Fig. 2).
 C. Mira, I. Gumowski and a Toulouse Research Group in the “prehistoric times of chaotic dynamics”, World Scientific Series in Nonlinear Science A, 39, 95-198, 2000.
 C. P. Pulkin, Oscillating iterated sequences (in Russian), Doklady Akademii Nauk SSSR, 76 (6), 1129-1132, 1950.
 C. Mira, Étude de la frontière de stabilité d’un point double stable d’une récurrence non linéaire autonome du deuxième ordre, Proceedings of the IFAC Symposium on Pulse-rate and Pulse-number Signals in Automatic Control, D 43-7II, 1968.Online