Brad, Interesting sequence! Please go ahead and submit it! Best regards Neil Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com On Wed, Jan 27, 2021 at 11:43 AM Brad Klee <bradklee@gmail.com> wrote:
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 _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun