Dynamical systems for quasiperiodic chains and new selfsimilar polynomials Dynamical systems in SL(2, R) or SL(2, C) naturally appear in the transfer matrix method for quasiperiodic chains characterized by arbitrary irrational numbers. We show new subdynamical systems and invariants that are related to full diagonal and offdiagonal components of the transfer matrices; they are analogous to formulae of Chebyshev polynomials of the first and second kinds. Applying them to an electronic problem on the Fibonacci chain, we obtain sets of selfsimilar polynomials, quasiperiodic extension of the Chebyshev polynomials of the first and second kinds with selfsimilar properties. Two scaling factors of the selfsimilarities coincide with ones obtained by the perturbative decimation renormalization group method. 
