The Fixed Point of a Generalization of the Renormalization Group Maps for Self-Avoiding Paths on Gaskets

摘要

Let W(x,y) = ax 3+ bx 4+ f 5 x 5+ f 6 x 6+ (3 ax 2)2 y+ g 5 x 5 y + h 3 x 3 y 2 + h 4 x 4 y 2 + n 3 x 3 y 3+a 24 x 2 y 4+a 05 y 5+a 15 xy 5+a 06 y 6, and X = $ X={frac{partial{W}}{partial{x}}}$ , $ Y={frac{partial{W}}{partial{y}}}$ , where the coefficients are non-negative constants, with a > 0, such that X 2(x,x 2)?Y(x,x 2) is a polynomial of x with non-negative coefficients.