|
|||||
|
|
Correlation dimension for iterated function systems |
|
| Authors: | Wai Chin Brian Hunt James A Yorke |
| Institution: | Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523 (On leave at: Institute for Mathematics and Its Applications, University of Minnesota, Minneapolis, Minnesota 55455) ; Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742 ; Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742 |
| Abstract: | The correlation dimension of an attractor is a fundamental dynamical invariant that can be computed from a time series. We show that the correlation dimension of the attractor of a class of iterated function systems in  is typically uniquely determined by the contraction rates of the maps which make up the system. When the contraction rates are uniform in each direction, our results imply that for a corresponding class of deterministic systems the information dimension of the attractor is typically equal to its Lyapunov dimension, as conjected by Kaplan and Yorke. |
| Keywords: | |
| 点击此处可从《Transactions of the American Mathematical Society》浏览原始摘要信息 | |
| 点击此处可从《Transactions of the American Mathematical Society》下载免费的PDF全文 | |