On Mitra's sufficient condition for topological chaos: Seventeen years later

This letter reports an easy extension of Mitra's “easily verifiable” sufficient condition for topological chaos in unimodal maps, and offers its application to reduced-form representations of two economic models that have figured prominently in the recent literature in economic dynamics: the check- and the M-map pertaining to the 2-sector Robinson-Solow-Srinivasan (RSS) and Matsuyama models respectively. A consideration of the iterates of these maps establishes the complementarity of the useful 2001 condition with the 1982 (LMPY) theorem of Li-Misiurewicz-Pianigiani-Yorke when supplemented by a geometric construction elaborated in Khan-Piazza (2011).