Abstract
Dynamical trace-map of the tight-binding model is investigated by generalizing the stacking rule of the Fibonacci lattice. The recurrence relation is defined by D ( n +1)= D ( n ) p D ( n -1) q for positive integers p and q , where D ( n ) is the atomic sequence of the n -th generation. The structure of the dynamical trace-map is analyzed in terms of the invariant and the quasi-invariant of the map. Characteristic features of the wave function, local density of states and the average density of states are analyzed.
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