ON THE STRUCTURE OF PERIODIC ORBITS ON A SIMPLE BRANCHED MANIFOLD

Itık, MEHMET; Banks, Stephen

doi:10.1142/s0218127410027842

ON THE STRUCTURE OF PERIODIC ORBITS ON A SIMPLE BRANCHED MANIFOLD

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS IN APPLIED SCIENCES AND ENGINEERING, cilt.20, sa.11, ss.3517-3528, 2010 (SCI-Expanded)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 20 Sayı: 11
Basım Tarihi: 2010
Doi Numarası: 10.1142/s0218127410027842
Dergi Adı: INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS IN APPLIED SCIENCES AND ENGINEERING
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Sayfa Sayıları: ss.3517-3528
Dokuz Eylül Üniversitesi Adresli: Evet

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.