Feigenbaum Julia Sets Concerning Renormalization Transformation
摘要
Considering long-range interaction model on generalized diamond hierarchical lattice, in this paper, we give a perfect description about the dynamical complexity of renormalization transformation Uτmnλ when λ is a natural number. In particular, we prove that the Julia sets of renormalization transformation Uτmnλ for certain positive real parameters τ are Feigenbaum Julia sets, which intersects with the positive real axis in a closed interval.