Abstract
We use a recently developed renormalization-group formalism to study the global properties of the period-doubling attractor. The renormalization scheme can be written in closed form in terms of universal functions. The results of the calculation appear as a smooth spectrum of scaling indices in full agreement with direct numerical calculations. As a special result we obtain the fractal dimension of the attractor to be =0.538 045 143 5, accurate to one part in . The only input for the calculation is the Taylor expansion of Feigenbaum’s universal function.
- Received 10 December 1985
DOI:https://doi.org/10.1103/PhysRevA.33.3622
©1986 American Physical Society