A computer-assisted proof of the existence of Smale horseshoe for the folded-towel map
arXiv:2101.10416 · doi:10.1016/j.cnsns.2020.105680
Abstract
The paper contains a rigorous proof of existence of symbolic dynamics chaos in the generalized Hénon map's 4th iterate , which was conjectured in the paper \textit{A 3D Smale Horseshoe in a Hyperchaotic Discrete-Time System} of Li and Yang, 2007. We prove also the uniform hyperbolicity of the invariant set with symbolic dynamics. The proofs are computer-assisted with the use of C++ library \textit{CAPD} for interval arithmetic, differentiation and integration.