I am trying to create an illustration for a paper and export it to PDF. Here is the code

```
textsize = 16;
Framed[Show[
  ContourPlot[y^2 - Cos[x], {x, -3 Pi, 3 Pi}, {y, -2.5, 2.5}, 
  ContourShading -> None, ContourStyle -> Thickness[0.002], 
PlotPoints -> 100, Frame -> None, Contours -> Range[-1, 7, 0.5], 
AspectRatio -> 4/(3 Pi), PlotRangePadding -> 0],

ContourPlot[y^2 - Cos[x] == 1, {x, -3 Pi, 3 Pi}, {y, -2.5, 2.5}, 
ContourShading -> None, ContourStyle -> Thickness[0.004], 
PlotPoints -> 200, Frame -> None, AspectRatio -> 4/(3 Pi), 
PlotRangePadding -> 0],

Graphics[{Black, Arrowheads[0.025], PointSize[0.0001], 
Thickness[0.0001], 
Arrow[#] & /@ {{{0.0, Sqrt[2]}, {0.35, 
    Sqrt[2]}}, {{-0.1, -Sqrt[2]}, {-0.35, -Sqrt[2]}}, {{2 Pi + 
     0.1, Sqrt[2]}, {2 Pi + 0.35, 
    Sqrt[2]}}, {{2 Pi - 0.1, -Sqrt[2]}, {2 Pi - 
     0.35, -Sqrt[2]}}, {{-2 Pi + 0.1, Sqrt[2]}, {-2 Pi + 0.35, 
    Sqrt[2]}}, {{-2 Pi - 0.1, -Sqrt[2]}, {-2 Pi - 
     0.35, -Sqrt[2]}}},
  Arrowheads[0.015], 
  Arrow[#] & /@  {{{0, 1}, {0.2, 
    1}}, {{-0, -1}, {-0.2, -1}}, {{2 Pi + 0.1, 1}, {2 Pi + 0.2, 
    1}}, {{2 Pi - 0.1, -1}, {2 Pi - 0.2, -1}}, {{-2 Pi + 0.1, 
    1}, {-2 Pi + 0.2, 1}}, {{-2 Pi - 0.1, -1}, {-2 Pi - 0.2, -1}}},
 Arrow[#] & /@  {{{0.1, 1.87}, {0.2, 
    1.87}}, {{-0.1, -1.87}, {-0.2, -1.87}}, {{2 Pi + 0.1, 
    1.87}, {2 Pi + 0.2, 
    1.87}}, {{2 Pi - 0.1, -1.87}, {2 Pi - 0.2, -1.87}}, {{-2 Pi + 
     0.1, 1.87}, {-2 Pi + 0.2, 
    1.87}}, {{-2 Pi - 0.1, -1.87}, {-2 Pi - 0.2, -1.87}}}    }],
Graphics[
Point[#] & /@ {{0, 0}, {Pi, 0}, {-Pi, 0}, {2 Pi, 0}, {-2 Pi, 0}}], 
Graphics[{Text[Style[0, textsize], {0, -0.4}], 
Text[Style[\[Pi], textsize], {Pi, -0.4}], 
Text[Style[-\[Pi], textsize], {-Pi, -0.4}], 
Text[Style[2 \[Pi], textsize], {2 Pi, -0.4}], 
Text[Style[-2 \[Pi], textsize], {-2 Pi, -0.4}]}], 
ImageSize -> 500]]

```

Then I use `Export[...,%]` on the result to create the PDF. Here is a part of it:

![enter image description here](https://i.stack.imgur.com/57t9c.png)

So, what's up with the little dots at the tips of the arrows? They are not visible in Mathematica and their size does not decrease if I decrease `Arrowheads`. They only solution I have found so far is take `Imagesize->1000` and then downscale the image in latex, which is not ideal because I need to control the line width across all images.

---

In short the problem can be reduced to:

```
Graphics[{Arrowheads@0.015, Arrow[{{-2 Pi - 0.1, -1}, {-2 Pi - 0.2, -1}}]}, 
  AspectRatio -> 4/(3 Pi), PlotRangePadding -> 0, 
  PlotRange -> {{-3 Pi, 3 Pi}, {-2.5, 2.5}}]

```

![enter image description here](https://i.stack.imgur.com/lwoQj.png)