Abstract
This paper considers the circle map at the special point: the one at which there is a trajectory with a golden mean winding number and at which the map just fails to be invertable at one point on the circle. The invariant density of this trajectory has fractal properties. Previous work has suggested that the global behavior of this fractal can be effectively analyzed using a kind of partition function formalism to generate anf versusα curve. In this paper the partition function is obtained by using a renormalization group approach.
Similar content being viewed by others
References
T. C. Halsey, M. H. Jensen, L. P. Kadanoff, I. Procaccia, and B. I. Shraiman,Phys. Rev. A, in press; U. Frisch and G. Parisi, in “Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics,” Varenna Summer School LXXXVIII, ed. M. Ghil, p. 84, North-Holland, New York (1985); R. Benzi, G. Paladin, G. Parisi, and A. VulpianiJ. Phys. A 17:3521 (1984).
M. H. Jensen, L. P. Kadanoff, A. Libchaber, I. Procaccia, and J. Stavans,Phys. Rev. Letts. 55:2798 (1985).
D. Rand, S. Ostlund, J. Sethna, and E. Siggia,Phys. Rev. Letts. 49:132 (1982);Physica 8D:303 (1983).
M. J. Feigenbaum, L. P. Kadanoff, and Scott J. Shenker,Physica 5D:370 (1982).
J. M. Greene,J. Math. Phys. 9:760 (1968);20:1181 (1982).
R. L. Devaney,Introduction to Chaotic Dynamical Systems (Benjamin-Cummins, 1985).
M. J. Feigenbaum,J. Stat. Phys. 19:15 (1978);21:669 (1979).
L. P. Kadanoff,Phys. Rev. Letts. 23:1641 (1981).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kadanoff, L.P. Renormalization group analysis of the global properties of a strange attractor. J Stat Phys 43, 395–410 (1986). https://doi.org/10.1007/BF01020644
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01020644