The secular evolution of extreme transneptunian objects with semi-major axes of 250 AU under the influence of hypothetical Planet Nine. Green curves for meta-stable objects, red curves for aligned objects, blue curves for anti-aligned objects, orange curve for circulating objects. Arrows shows direction of evolution with time. Above black curve orbits intercept that of Planet Nine.
<a href="//commons.wikimedia.org/w/index.php?title=User:Agmartin&amp;action=edit&amp;redlink=1" class="new" title="User:Agmartin (page does not exist)">Agmartin</a> based on data from <a rel="nofollow" class="external text" href="https://arxiv.org/pdf/1710.01804.pdf">Figure 2 of Batygin and Morbidelli 2017</a>
CC BY-SA 4.0
I used Excel to roughly sketch curves of the Hamiltonian plotted in <a rel="nofollow" class="external text" href="https://arxiv.org/pdf/1710.01804.pdf">Figure 2 of Batygin and Morbidelli 2017</a>