ON THE STRUCTURE OF PERIODIC ORBITS ON A SIMPLE BRANCHED MANIFOLD


Itik M. , Banks S. P.

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, cilt.20, ss.3517-3528, 2010 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 20 Konu: 11
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1142/s0218127410027842
  • Dergi Adı: INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
  • Sayfa Sayıları: ss.3517-3528

Özet

We study the structure of the periodic orbits on a simple branched manifold which is a subtemplate of the branched manifold of the chaotic attractor that is obtained from a cancer model. We indicate the conditions for the knotted and linked periodic orbits by using symbolic dynamics, then we extend the results to the periodic solutions of the chaotic attractor. Furthermore, we compare the knots obtained by using same symbol sequences for the simple branched manifold and the attractor's branched manifold by using a knot invariant, specifically, we calculate the Kauffman bracket polynomial. In order to count the number of closed curves which is required to calculate the bracket polynomial we propose a new method which uses cyclic permutations.