21 October, 2026

Notes

2026-10-30

To do!

• So now that I have a general idea, how the phase space is changing in between \(E \in (-0.5, -0.3)\) I am now curious to see how the indiviual trajectories for the interesting periodic orbits behave
  • follow periodic orbit for period=1, 3
    • phase space
    • configuration space

naming of periodic orbits

So I am currently studying two specific periodic orbits. I call these orbit ‘A’. There is one which is there from \(E = -\infty\) and has a period of \(p=1\), in the sense of poincaré maps, \(M:\Sigma -> \Sigma\). Hence the name of that orbit \(A1\).

Then there is a periodic orbit, with period \(p=3\). Its origin is yet unknown, but seems to come into existance, due to the ‘detection’ of one outer wall.

Lost Wonderers Thoughts: