Efficient Automation of Index Pairs in Computational Conley Index Theory

@article{Frongillo2012EfficientAO,
  title={Efficient Automation of Index Pairs in Computational Conley Index Theory},
  author={Rafael M. Frongillo and Rodrigo Trevi{\~n}o},
  journal={SIAM J. Appl. Dyn. Syst.},
  year={2012},
  volume={11},
  pages={82-109}
}
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 semi-conjugacies from a map on a manifold to a subshift of finite type. We apply these new algorithms to the standard map at different values of the perturbative parameter {\epsilon} and obtain rigorous lower bounds for its topological entropy for {\epsilon} in [.7, 2]. 

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