Strange attractor of Henon map and its basin (Q1805389)

The Henon map \(T_{a,b} (x,y) = (1 - ax^ 2 + y, bx)\) is considered. The author constructs a trapping region \(G\) of topologically transitive strange attractor \(\Lambda_{a,b}\) for \(T_{a,b}\), and proves that \(\Lambda_{a,b} = \bigcap_{n \geq 0} T^ n_{a, b} G\). Consequently the truth of the conjecture of \textit{M. Benedicks} and \textit{L. Carleson} [Ann. Math., II. Ser. 133, No. 1, 73-169 (1991; Zbl 0724.58042)] about the basin of a strange attractor is proved.