Third-order renormalization-group calculation of the Feigenbaum universal bifurcation ratio in the transition to chaotic behavior
- 1 February 1982
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 25 (2) , 1196-1198
- https://doi.org/10.1103/physreva.25.1196
Abstract
Using the renormalization-group method of Derrida, Gervois, and Pomeau, we have extended the calculation of the Feigenbaum universal bifurcation ratio to third order. The calculated values for the limit point and the bifurcation ratio are, respectively: and , which agree extremely well with the exact values: and .
Keywords
This publication has 11 references indexed in Scilit:
- Dissipative bifurcation ratio in the area-non-preserving Henon mapJournal of Physics A: General Physics, 1981
- Transition to Chaotic Behavior via a Reproducible Sequence of Period-Doubling BifurcationsPhysical Review Letters, 1981
- A SUBHARMONIC ROUTE TO TURBULENT CONVECTION*Annals of the New York Academy of Sciences, 1980
- Feigenbaum's ratios of two-dimensional area preserving mapsPhysics Letters A, 1980
- Period doubling and the onset of turbulence: An analytic estimate of the Feigenbaum ratioPhysics Letters A, 1980
- The universal metric properties of nonlinear transformationsJournal of Statistical Physics, 1979
- Universal metric properties of bifurcations of endomorphismsJournal of Physics A: General Physics, 1979
- Rayleigh-Bénard experiment in liquid helium ; frequency locking and the onset of turbulenceJournal de Physique Lettres, 1979
- Quantitative universality for a class of nonlinear transformationsJournal of Statistical Physics, 1978
- On finite limit sets for transformations on the unit intervalJournal of Combinatorial Theory, Series A, 1973