## The dimension of chaotic attractors.(English)Zbl 0561.58032

Order in chaos, Proc. int. Conf., Los Alamos/N.M. 1982, Physica D 7, 153-180 (1983).
[For the entire collection see Zbl 0536.00007.]
The authors review most of the notions of dimension for chaotic attractors that are in current use, describe rigorous and numerical results on the relations between different types of dimension, and formulate the conjecture that for typical chaotic attractors all dimensions defined by purely metric properties take on a common value (the ”fractal dimension”), while on the other hand frequency dependent dimensions take on a (generally different) common value. They support this conjecture by numerical computations on a class of generalized baker’s transformations. The frequency dependent dimensions typically coincide with the Lyapunov-dimension. The feasability of computing the different dimension numbers is discussed. The reader might wish to compare these results to those obtained by P. Grassberger and I. Procaccia [Physica D 9, 189–208 (1983; Zbl 0593.58024)] where a further frequency dependent dimension number is defined.
Reviewer: G.Keller

### MSC:

 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior 37A05 Dynamical aspects of measure-preserving transformations 28D05 Measure-preserving transformations 37D99 Dynamical systems with hyperbolic behavior

### Citations:

Zbl 0536.00007; Zbl 0593.58024

### References:

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