Tweaked first figure, and added another depicting a Stokes point.

6 files changed, 45 insertions, 42 deletions

diff --git a/figs/antithimble_homology.eps b/figs/antithimble_homology.eps
index 87a534c..e1907ec 100644
--- a/figs/antithimble_homology.eps
+++ b/figs/antithimble_homology.eps
@@ -1,6 +1,6 @@
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diff --git a/figs/thimble_homology.eps b/figs/thimble_homology.eps
index e3b1fd7..28904a1 100644
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+++ b/figs/thimble_homology.eps
@@ -1,11 +1,11 @@
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@@ -5275,13 +5265,6 @@ BT
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diff --git a/figs/thimble_stokes_1.pdf b/figs/thimble_stokes_1.pdf
new file mode 100644
index 0000000..d291173
--- /dev/null
+++ b/figs/thimble_stokes_1.pdf
diff --git a/figs/thimble_stokes_2.pdf b/figs/thimble_stokes_2.pdf
new file mode 100644
index 0000000..30cdb9a
--- /dev/null
+++ b/figs/thimble_stokes_2.pdf
diff --git a/figs/thimble_stokes_3.pdf b/figs/thimble_stokes_3.pdf
new file mode 100644
index 0000000..d6a19c7
--- /dev/null
+++ b/figs/thimble_stokes_3.pdf
diff --git a/stokes.tex b/stokes.tex
index 4c1a882..6485ed7 100644
--- a/stokes.tex
+++ b/stokes.tex
@@ -257,6 +257,26 @@ called \emph{Stokes points}, and the gradient descent trajectories that join
 two stationary points are called \emph{Stokes lines}. An example of this
 behavior can be seen in Fig.~\ref{fig:1d.stokes}.
 
+\begin{figure}
+  \includegraphics{figs/thimble_stokes_1.pdf}\hfill
+  \includegraphics{figs/thimble_stokes_2.pdf}\hfill
+  \includegraphics{figs/thimble_stokes_3.pdf}
+
+  \caption{
+    An example of a Stokes point. (Left) The collection of thimbles necessary
+    to progress around from left to right, highlighted in a darker color, is
+    the same as it was in Fig.~\ref{fig:thimble.homology}. (Center) The thimble
+    $\mathcal J_\blacklozenge$ intersects the stationary point $\blacktriangle$
+    and its thimble, leading to a situation where the contour is not easily
+    defined using thimbles. This is a Stokes point. (Right) The Stokes point
+    has passed, and the collection of thimbles necessary to produce the path
+    has changed: now $\mathcal J_\blacktriangle$ must be included. Notice that
+    in this figure, because of the symmetry of the pure models, the thimble
+    $\mathcal J_\blacksquare$ also experiences a Stokes point, but this does
+    not result in a change to the path involving that thimble.
+  } \label{fig:1d.stokes}
+\end{figure}
+
 The prevalence (or not) of Stokes points in a given continuation, and whether
 those that do appear affect the weights of critical points of interest, is a
 concern for the analytic continuation of theories. If they do not occur or