Power-law sensitivity to initial conditions within a logisticlike family of maps: Fractality and nonextensivity

@article{Costa1997PowerlawST,
  title={Power-law sensitivity to initial conditions within a logisticlike family of maps: Fractality and nonextensivity},
  author={U. Costa and M. Lyra and A. Plastino and C. Tsallis},
  journal={Physical Review E},
  year={1997},
  volume={56},
  pages={245-250}
}
Power-law sensitivity to initial conditions, characterizing the behaviour of dynamical systems at their critical points (where the standard Liapunov exponent vanishes), is studied in connection with the family of nonlinear 1D logistic-like maps $x_{t+1} = 1 - a | x_t |^z, (z > 1; 0 0} \Delta x(t) / \Delta x(0)} = [1+(1-q)\lambda_q t]^{1/(1-q)}$ (equal to $e^{\lambda_1 t}$ for q=1, and proportional, for large t, to $t^{1/(1-q)}$ for $q \ne 1; q \in R$ is the entropic index appearing in the… Expand
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