Renormalization group structure for sums of variables generated by incipiently chaotic maps

We look at the limit distributions of sums of deterministic chaotic variables in unimodal maps and find a remarkable renormalization group (RG) structure associated with the operation of increment of summands and rescaling. In this structure-where the only relevant variable is the difference in control parameter from its value at the transition to chaos-the trivial fixed point is the Gaussian distribution and a novel nontrivial fixed point is a multifractal distribution that emulates the Feigenbaum attractor, and is universal in the sense of the latter. The crossover between the two fixed points is explained and the flow toward the trivial fixed point is seen to be comparable to the chaotic band merging sequence. We discuss the nature of the central limit theorem for deterministic variables. Fil: Fuentes, Miguel Angel. Santa Fe Institute; Estados Unidos. Comisión Nacional de Energía Atómica. Gerencia del Área de Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Bariloche); Argentina. Pontificia Universidad Católica de Chile; Chile. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina Fil: Robledo, Alberto. Universidad Nacional Autónoma de México; México