deletions | additions       diff --git a/Measuring distances on the phase plane.tex b/Measuring distances on the phase plane.tex  index e4659bd..9f9b100 100644  --- a/Measuring distances on the phase plane.tex  +++ b/Measuring distances on the phase plane.tex 
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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: 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 in order to do meaningful comparison between the distances to our $2:1$ and $1:1$ attractors we rescaled the distances as $D \rightarrow p_2 D$.