View source for Talk:Attractor dimensions

==Reviewer A==

The review is, of course, scientifically sound, my remarks point in the direction of easier readability, and more illustrations only.

At the very beginning, the presentation of a plot of a factal  chaotic attractor would be enlightening.

I would recommend to start the section 'Box counting dimension' with a more qualitative picture, by just recalling the relation <math>N(\epsilon) \sim \epsilon^{-D_0}</math> and giving an example of the <math>\ln N(\epsilon)</math> vs <math>\ln(1/\epsilon)</math> plot. It might be worth mentioning that this <math>D_0</math> is also called the fractal dimension.

Section 'The natural measure' I would recommend to start with a
qualititve description of the fact that on any attractor a natural
distribution develops which is the probability that a certain part
of the attractor is visited by the long term dynamics. Here a spatial
view of a natural distributon would be very useful, whch could also be
used to motivate the need for a fractal characterization of such
disribution. (If needed, it would be a pleasure for me to provide
such a figure.)

In 'The Renyi Dimension D_q' section the alternative term of
generalized dimensions could be mentioned.

In the section on 'Lyapunov dimension ..' I recommend first to give
the result for two-dimensional maps (or three-dimensional flows):
:<math>D_L=1-\lambda_1/\lambda_2</math>,
which is much easier, and this can then be followed by (6).

As for references, the author might wish to add
Beck, Schlogl: Thermodynamics of Chaotic Systems, CUP, 1993
in relation to Renyi dimensions, and
Tel, Gruiz: Chaotic Dynamics, CUP 2006
as a recent book on chaos and transient chaos.

Thank you for your help.