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I have some questions about the Henon map that are not clear for me. I have seen that the correlation dimension of the Henon map is approximately 1,21, is that measure similar to its fractal dimension?

Also, can the Henon map could be considered like a multifractal? I am using a program that measures the multifractal spectra and the maximum value of Q, sometimes it is 1,21, when I rerun the program it can be 1,27 and when I run it again it can be also 1,31, why is that change?

That multifractal program measures the multifractal spectra based on the figure of the henon map

Any help?

Lila
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1 Answers1

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The maximum value of of the f(alpha) spectrum occurs at the value of alpha for which Q=0. The alpha(Q) spectrum is numerically derived from the generalized dimension spectrum, D(Q). The D(Q) spectrum is calculated from the slope of a log-log plot of experimental data (related to the sum over some probability distribution raised to the power Q vs boxsize).

The value of the maximum can change depending on which portion of data is linearly fit, as the slope of the line will be different.

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