title: Universal renormalization-group dynamics at the onset of chaos in logistic maps and nonextensive statistical mechanics.
abstract: We uncover the dynamics at the chaos threshold mu infinity of the logistic map and find that it consists of trajectories made of intertwined power laws that reproduce the entire period-doubling cascade that occurs for mu<mu infinity. We corroborate this structure analytically via the Feigenbaum renormalization-group (RG) transformation and find that the sensitivity to initial conditions has precisely the form of a q exponential, of which we determine the q index and the q-generalized Lyapunov coefficient lambda(q). Our results are an unequivocal validation of the applicability of the nonextensive generalization of Boltzmann-Gibbs statistical mechanics to critical points of nonlinear maps.
authors.affiliation: Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro, RJ, Brazil. baldovin@cbpf.br
authors.forename: F
authors.initials: F
authors.lastname: Baldovin
authors.forename: A
authors.initials: A
authors.lastname: Robledo