Feigenbaum Julia Sets Concerning Renormalization Transformation

Abstract

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 U_τmnλ when λ is a natural number. In particular, we prove that the Julia sets of renormalization transformation U_τmnλ for certain positive real parameters τ are Feigenbaum Julia sets, which intersects with the positive real axis in a closed interval.

Keywords

Renormalization transformation / Feigenbaum Julia set / glass transition

References

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