Resumen
It is known that the famous Feigenbaum–Coullet–Tresser period doubling universality has a counterpart for area-preserving maps of . A renormalization approach has been used in Eckmann et al (1982 Phys. Rev. A 26 720–2) and Eckmann et al (1984 Mem. Am. Math. Soc. 47 1–121) in a computer-assisted proof of existence of a 'universal' area-preserving map F*—a map with orbits of all binary periods . In this paper, we consider maps in some neighbourhood of F* and study their dynamics. We first demonstrate that the map F* admits a 'bi-infinite heteroclinic tangle': a sequence of periodic points {zk}, , whose stable and unstable manifolds intersect transversally; and, for any , a compact invariant set on which F* is homeomorphic to a topological Markov chain on the space of all two-sided sequences composed of N symbols. A corollary of these results is the existence of unbounded and oscillating orbits. We also show that the third iterate for all maps close to F* admits a horseshoe. We use distortion tools to provide rigorous bounds on the Hausdorff dimension of the associated locally maximal invariant hyperbolic set: