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

Abstract

The paper contains a rigorous proof of existence of symbolic dynamics chaos in the generalized Hénon map’s 4th iterate H4, which was conjectured in the paper 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 CAPD for interval arithmetic, differentiation and integration.