The global bifurcation structure of a kind of digit mapping

Abstract

The global structure of the mapping T_n:x→[x ²]_n is studied. The symmetric unconnected substructures of T₂ is coincident with [1] by computer, but for n=3 the symmetry of these substructures vanishes. As n is increasing, the global bifurcation structure of T_n is shown. Finally, similar results for the mapping T_{n, μ}:x→[μx ²]_n are also proved..