Uniform hyperbolicity of locally maximal chaotic invariant sets in a system with only one stable equilibrium*

By the methods of Poincaré map and the cone field theory, we present a rigorous computer-assisted method to verify the existence of a locally maximal uniformly hyperbolic chaotic invariant set for an autonomous chaotic system which has only one stable equilibrium. At the same time, our arguments show that the second return Poincaré map restricted to the hyperbolic set is indeed topologically conjugate to the 2-shift map.