EQUIVALENCE BETWEEN THE NIELSEN AND THE SCALING TRANSFORMATIONS IN ONE-DIMENSIONAL QUASI-PERIODIC SYSTEMS

An equivalence between the Nielsen transformations in mathematics and the scaling, transformations in quasiperiodic physics in one dimension is shown herein. By recognizing this equivalence one becomes able to obtain the trace map for the quasiperiodic lattices constructed by an arbitrary number of atoms in the chain, where the atoms are symbolized by letters. In this approach the scaling transformations are regarded as the automorphisms of the set of letters, which induce the trace map as the inner automorphisms.