Dimensions and entropies of strange attractors from a fluctuating dynamics approach
Abstract
It is shown that the fluctuations in the divergence of near-by trajectories on (strictly deterministic) strange attractors can be modelled by stochastic concepts. In particular, we propose Kramers-Moyal type equations for correlation functions between points on the attractor. The drift terms are the Lyapunov exponents, the diffusion terms depend on the above fluctuations. From this, we obtain bounds on generalized dimensions and entropies. Numerical results show that in nearly all studied cases (Hénon map, Zaslavskii map, Mackey-Glass eq.) the attractors are fractal measures in the sense of Farmer (information dimension ≠ Hausdorff dimension; metric entropy ≠ topological entropy).
- Publication:
-
Physica D Nonlinear Phenomena
- Pub Date:
- August 1984
- DOI:
- Bibcode:
- 1984PhyD...13...34G