Efficient Automation of Index Pairs in Computational Conley Index Theory

Abstract

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 values of the perturbative parameter $\varepsilon$ and obtain rigorous lower bounds for its topological entropy for $\varepsilon\in[.7,2]$.