26 Jan
2021
26 Jan
'21
6:02 p.m.
Section 4 of this student paper has a nice tabulation of periodic orbits on the Rössler attractor: http://chaosbook.org/projects/Carroll/Carr12.pdf We probably would want to define a sequence:
a(n) counts the number of distinct cycles of winding number n on the Rössler attractor with (a,b,c)=(.2,.2,5.7).
For the numbers a(n), from n=1, I calculated that: a(n) = 1, 1, 2, 1, 2, 3, 4, 6, 8, 10, 17 . . . These were determined using a numerical algorithm with randomized searching across a linear Poincare section. If there are hidden cycles, which are difficult to reach by iterating Newton's method, I'm worried these numbers could be wrong. Does anyone else get the same or better than? --Brad