Horseshoes and the Conley index spectrum. II: The theorem is sharp (Q1576835)

In a series of papers Mrozek and the present authors with coauthors proved that an isolated invariant set is semiconjugate to the full shift dynamics on two symbols. The authors show which spectra are possible and then produce examples which clearly delineate which spectral conditions do or do not allow one to conclude the existence of a horseshoe. Moreover the authors show that the results mentioned above cannot be generalized further.