Chaotic behavior in the Helleman mapping (Q1096945)

The purpose of this paper is to obtain a sufficient condition, satisfied by a pair of parameters, for which a two-dimensional real quadratic diffeomorphism has the qualitative properties of the Smale horseshoe. This diffeomorphism is called here ``Helleman mapping'', which is only a variant of the known Hénon map. In the case of the Hénon map, the result of the author can be compared with those of other authors, not quoted [see, e.g., \textit{R. Devaney} and \textit{Z. Nitecki}, Commun. Math. Phys. 67, 137-146 (1979; Zbl 0414.58028); \textit{H. El Hamouly} and the reviewer, C. R. Acad. Sci., Paris, Sér. I 293, 525-528 (1981; Zbl 0482.58025); \textit{P. Holmes} and \textit{D. Whitley}, Phil. Trans. R. Soc. Lond., A 311, 43-102 (1984; Zbl 0556.58023)].