Coefficient scaling.
We prove a remarkably simple but powerful recursion relation for the coefficients of iterated polynomials. We also prove that the recursion relation holds for the coefficients of certain functions of the iterated polynomial. Using the recursion relations, we obtain a closed-form expression for the average number of closed-loop self-avoiding walks per site on a family of fractal lattices. We describe numerical results, which exhibit log-periodic oscillations, and find good agreement between these results and the theory developed here, which predicts the existence of the log-periodic oscillations and their amplitudes. Finally, we discuss insights gained into the mathematical origins of critical phenomena.
Paul
G
G
gerry@argento.bu.edu