Abstract
Power-law sensitivity to initial conditions, characterizing the behavior of dynamical systems at their critical points (where the standard Liapunov exponent vanishes), is studied in connection with the family of nonlinear one-dimensional logisticlike maps ( ). The main ingredient of our approach is the generalized deviation law (equal to for and proportional, for large to for is the entropic index appearing in the recently introduced nonextensive generalized statistics). The relation between the parameter and the fractal dimension of the onset-to-chaos attractor is revealed: appears to monotonically decrease from 1 (Boltzmann-Gibbs, extensive, limit) to when varies from 1 (nonfractal, ergodiclike, limit) to zero.
- Received 6 January 1997
DOI:https://doi.org/10.1103/PhysRevE.56.245
©1997 American Physical Society