“…In [33,35], an algorithm is developed for the construction of a combinatorial index pair (P 1 , P 2 ) such that P 1 \ P 2 contains an apriori given set Q ⊂ H. Given an approximate rough covering Q ⊂ H of a hypothetic periodic trajectory observed in numerical simulations, one can use the algorithm for the construction of a combinatorial index pair containing Q mentioned in Section 3.5 for a representation F of the map ϕ t computed with the use of the software [7] for some apriori chosen t > 0. If the algorithm succeeds then it constructs a combinatorial index pair (P 1 , P 2 ) such that N := |P 1 \ P 2 | is an isolating neighborhood with respect to ϕ t , and the homological Conley index of N with respect to ϕ t can be automatically computed with algorithms available in [8,29,36]. By Lemma 3.5, N is an isolating neighborhood also for the flow ϕ, and S := inv(N, ϕ t ) = inv(N, ϕ).…”