Multifractal structure of a riddled basin.
For a two-dimensional piecewise linear map with a riddled basin, a multifractal spectrum f(gamma), which characterizes the "skeletons" of the riddled basin, is introduced. With f(gamma), the uncertainty exponent is obtained by a variational principle, which enables us to introduce a concept of a "boundary" for the riddled basin. A conjecture on the relation between f(gamma) and the "stable sets" of various ergodic measures, which coexist with the natural invariant measure on the chaotic attractor, is also proposed. (c) 2001 American Institute of Physics.
Suetani
Hiromichi
H
Department of Applied Analysis and Complex Dynamical Systems, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, JapanThe Institute of Statistical Mathematics, Tokyo 106-8569, Japan.
Horita
Takehiko
T