Strange Objects in the Complex Plane

TitleStrange Objects in the Complex Plane
Publication TypeJournal Article
Year of Publication1983
AuthorsWidom, M., Bensimon D., Kadanoff L. P., & Shenker S.
Published inJournal of Statistical Physics
Issue3
Page(s)443-454
Other Numbers3493
Abstract

Julia sets are examined as examples of strange objects which arise in the study of long time properties of simple dynamical systems. Technically they are the closure of the set of unstable cycles of analytic maps. Physically, they are sets of points which lead to chaotic behavior. The mapf(z)=z2+p is analyzed for smallp where the Julia set is a closed curve, and for largep where the Julia set is completely disconnected. In both cases the Hausdorff dimension is calculated in perturbation theory and numerically. An expression for the rate at which points escape from the neighborhood of the Julia set is derived and tested in a numerical simulation of the escape.

Bibliographic Notes

Journal of Statistical Physics, Volume 32, No. 3, pp. 443-454

Abbreviated Authors

M. Widom, D. Bensimon, L. P. Kadanoff, and S. Shenker

ICSI Research Group

Networking and Security

ICSI Publication Type

Article in journal or magazine