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jBillou edited Measuring distances on the phase plane.tex
about 9 years ago
Commit id: f34a49c6e02f453e82b50795346a6e181a994e02
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D = 1/N_t \sum_{t=1}^{N_t} \min_k \| \Gamma(k)-(\theta_t,\phi_t)\|
\end{equation}
However, in order to compare the distances from a trace to a $p_1:1$ attractor and the distance from a trace to a $p_2:1$ attractor a correction need to be taken into account. Indeed as a $p_2:1$ attractor is dividing the phase plane into $p_2+1$ regions the average distance (integrated over the plane) to the attractor is inversely proportional to $p_2$. For that reason
a traces will always be closer to higher order mode locked attractors (e.g.
$10:1$), thus $10:1$). Thus in order to do meaningful comparison between the distances to our $2:1$ and $1:1$ attractors we rescaled the distances as $D \rightarrow p_2 D$.