Adaptive Set-Oriented Computation of Topological Horseshoe Factors in Area and Volume Preserving Maps

We describe an automatic chaos verification scheme, based on set-oriented numerical methods, which is especially well suited to the study of area- and volume preserving diffeomorphisms. The novel feature of the scheme is an iterative algorithm for approximating connecting orbits between collections of hyperbolic fixed and periodic points with greater and greater accuracy. The algorithm is geometric rather than graph theoretic in nature and, in contrast to existing methods, does not require the computation of chain recurrent sets. We provide several example computations in dimensions two and three.

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