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The aim of this paper is to introduce a method for computing rigorous lower bounds for topological entropy. The topological entropy of a dynamical system measures the number of trajectories that separate in finite time and quantifies the complexity of the system. Our method relies on extending existing computational Conley index techniques for constructing… (More)

We present new methods of automating the construction of index pairs, essential ingredients of discrete Conley index theory. These new algorithms are further steps in the direction of automating computer-assisted proofs of semiconjugacies from a map on a manifold to a subshift of finite type. We apply these new algorithms to the standard map at different… (More)

- Rodrigo Treviño
- 2014

Let (S, α) be a flat surface. By that I mean that S is a Riemann surface and α a 1-form on S which is holomorphic. That this defines a flat surface is a standard fact; one can consult Zorich's excellent introduction to the area to see how this is done [7]. The form α defines two dynamical systems on S, called the horizontal and vertical flows. One obtains… (More)

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