Practical considerations on the calculation of the uncertainty exponent and the fractal dimension of basin boundaries. (English) Zbl 0876.58026
Summary: The calculation of the uncertainty exponent as defined by C. Grebogi, S. W. McDonald, E. Ott, and J. A. Yoshe [Phys. Lett. A 99, No. 9, 415-418 (1983)] is examined in detail, and it is modified to provide a more robust estimate of the fractal dimension of basin boundaries. Practical considerations of using the uncertainty exponent method are provided.
MSC:
| 37C70 | Attractors and repellers of smooth dynamical systems and their topological structure |
| 28A25 | Integration with respect to measures and other set functions |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
