A computer-assisted proof of the existence of Smale horseshoe for the folded-towel map (Q2656034)

The author considers the dynamical system defined by the map \(H(x,y,z)=(1.76-y^{2}-0.1z, x, y)\). She provides a rigorous proof for the existence of symbolic dynamics chaos in the generalized Hénon map's 4-th iterate \(H^{4}\), thus confirming a conjecture by \textit{Q. Li} and \textit{X.-S. Yang} [Discrete Dyn. Nat. Soc. 2007, Article ID 16239, 9 p. (2007; Zbl 1179.37050)]. Further, the author shows the uniform hyperbolicity of the invariant set. The computer-assisted proofs make use of the C++ library CAPD for interval arithmetic, differentiation and integration. The author also presents several plots to support the theoretical findings.